Annual Report

Annual Report

National Center for Theoretical Sciences

October 2008

Annual Report

National Center for Theoretical Sciences 101, Section 2, Kuang Fu Road, Hsinchu, Taiwan 30013

Mathematics Division

Tel: 886-3-5728263 Fax: 886-3-5728161 e-mail: [email protected] http://www.math.cts.nthu.edu.twl

Physics Division

Tel: 886-3-5734969 Fax: 886-3-5735086 e-mail: [email protected] http://phys.cts.nthu.edu.tw

October 2008

Annual Report

National Center for Theoretical Sciences

October 2008

I.

Words from the Director -----

1

II. Mathematics Division ---------

2

Report of the Division Head ------------------- 3 Executive Committee Members --------------- 5 Academic Committee Members --------------- 6 Highlights of the Programs --------------------- 7 Activities of Onsite Scientists ------------------ 50 Preprints ------------------------------------------- 61 Appendix ------------------------------------------ 69 I. Visiting Mathematicians -------------------- 69 II. Conference, Workshop & School ---------- 79

III. Physics Division

------------------- 85

Report of the Division Head ------------------ 86 Highlights of Programs ------------------------ 92 Focus Group Complex System ------------------------------- 92 Condensed Matter Physics ------------------- 95 Particles and Fields ---------------------------- 107 Interdisciplinary Fields ------------------------ 126 Working Group Plasma Science --------------------------------- 134 Softmatter and Nonlinear Physics ----------- 138 Research Activities of Individuals ------------ 144 Introducing New Members -------------------- 183

Annual Report National Center for Theoretical Sciences October 2008

Publisher:

Editors:

Jing Yu

Mandy Chen ( Mathematics Division) Sherry Pang(Physics Division)

Words from the Director he second phase of NCTS operation starts from January 2004 till December 2008. This is the last year. National Science Council (NSC) has conducted an on-site review of NCTS this January. Basing on the report of the review committee, and the suggestion of the steering committee of NCTS, the NSC made the decision in July, to continue supporting NCTS with a third phase operation, from January 2009 to December 2014. The basic operating framework remains the same, with main project at Hsinchu, cohosted by NTHU, NCTU, and NCU, one subproject at Taipei hosted by NTU, and another subproject in southern Taiwan cohosted by NCKU and NSYSU. The detailed proposal for the 3rd phase is being worked out by all participating parts at this moment. This year we enjoyed the newly expanded and renovated space of the headquarter of NCTS at the campus of NTHU. Located on the 4-th and 5-th floor of the 3rd general building, this expanded space puts the Physics Division and the Mathematics Division under one roof, working more closely together. The new 1st guest house of NTHU, after one year running, also was highly acclaimed by all our visitors. There is yet another new guest house of TCTU nearby. Thus as far as hardware is concerned, we are ready to enter into the 3rd phase of NCTS. We continue our efforts of promoting

interdisciplinary researches in theoretical sciences. Besides Mathematical Biology, Bioinformatics, and Biological Physics in which focus programs are actively going on, a new initiative this year is in the direction of theoretical Statistics. In the subproject at NCKU, a program on Statistics methods including Biostatistics has been implemented and well received. In 2009, further interdisciplinary program relating to theoretical Statistics are expected to be incorporated into the main project. We anticipate that new international research team in this direction will also be formed in the near future. When NCTS started its operation 11 years ago, one of its mission in our mind is to modify the landscape of theoretical sciences research in Taiwan. On the international stages, there were important research areas in which Taiwanese scientists didn't take part. We made efforts and we now see some changes. Mathematical Physics is one such area. Dynamical Systems is another. In the direction of interdisciplinary researches, theoretical sciences relating to Biology is also becoming an important trend in Taiwan. New research groups started to form, existed research groups become more established, as the on-site review committee remarked in January. We look forward to another 10 years of NCTS with success.

1 ‹‹- Words from the Director

Mathematics Division

Report of the Division Head his is the last year of the 2nd phase operation of NCTS. We are now planning a detailed proposal for the 3rd phase of NCTS, 2009-2014, and looking forward to further develop the roles play by NCTS in the global mathematics research. On the one hand, we are searching for the new division head to lead NCTS. On the other hand, we are considering new strategies and initiatives which can bring us to new grounds. There was an on-site review of NCTS conducted by an international committee in January 2008. The report of this committee on the mathematics division is very positive and encouraging. In the main project, the three hosting universities now offers 15 center scientists positions for the mathematics division. In 2008, we have five from NCTU, three from NTHU, and two from NCU. Among them, one in Algebraic Geometry, one in Algebraic Topology, one in Classical Analysis, three in Dynamical Systems, two in Number Theory, and one in Scientific Computation. We have committed firmly to the cultivation and support of young generations. In last decade the summer internship program at NCTS grows steadily, those undergraduate interns of past years now studies in top graduate schools of the States, Europe, as well as in Taiwan. Past research assistants (one year position at NCTS) are becoming post doctors or young faculties in Taiwan after getting their Ph. D. degrees from great universities abroad. Besides (partially) supporting graduate students to attend important international summer/winter schools, e.g. Fields Institute

(Canada) and Arizona Arithmetic Geometry Center this year, we also supported two advanced students to do research abroad for three months, one at Max-Planck Institute (Bonn), the other one at Fields Intitute (with local expenses supported by Fields). Another initiative this year is a Taiwan-Tohoku workshop supported by NCTS in April, organized by E. Yanagida (Tohoku U.), and Jann-Long Chen (NCU), with two Ph.D. students from Taiwan visiting Tohoku, interacting with Ph.D. students on differential equations in Tohoku U. The second round will be in Jan. 2009, to be held at NCTS, with 6 Japanese Ph.D. students coming interacting with our Ph.D. students of differential equations. These are a bilateral activities, each side pays their own air tickets. Papers from NCTS Math Preprint Series of previous years continue to appear in important international journals. We are happy to report, in particular, the paper: Elliptic Functions, Green Function, and the Mean Field Equation on Tori, by Chang-Shou Lin and Chin-Lung Wang had recently been accepted by Annals of Math. This paper was singled out in 2006 NCTS report as important breakthrough. It is also the third paper from NCTS in two years accepted by the prestigious Ann. Math. Mathematics papers usually take a longer period for refereeing than papers from other fields, for a preprint to appear in print one may need more than two years after it is submitted. Submitting to top journals usually take more time. On the other hand, mathematics works also need more years to have its impact fully come out. The AMS

3 ‹‹- Report of the Division Head

Math SciNet therefore keeps track a record of all the important math journals, counting citations of five years, as contrast to the SCI impact factors which count citations only in two years. In the on-site review report this year, the following research contributions were highlighted : (a) A sharp bound for the pluri-canonical map to be rational for threefolds which are either of general type or Fano. (b) Invariance of the quantum cohomology ring after analytic continuation on the Kähler moduli. (c) An important result on the three body problem by the variational method. (d) Determined all algebraic relations among special zeta values and gamma values in positive characteristic. Since the five year five million project of the Ministry of Education started two years ago, the leading research universities in Taiwan have put more resources into basic theoretical sciences. This is very encouraging. At National Taiwan University, the Taida Institute of Mathematical Sciences TIMS was established, with Chang-Shou Lin, previous director of NCTS, as director. At National Tsing Hua University, CMS, a Center for Mathematical Sciences founded with Sze-Bi Hsu as director, and at National Central University, also a Center for Mathematics and Theoretical Sciences was set up, with Y. R. Lin-Liu as director. TIMS with fully support from NTU is particularly active, with many seminars, courses going on, covering a wide

Report of the Division Head -›› 4

range of pure and applied mathematics. NCTS is happily cooperating with all these university institutions, working together for the common goal of developing theoretical sciences in Taiwan. However, the role of NCTS is also distinct from and complement to these university institutions. The population of mathematicians in Taiwan as compared to the total population, is still far below the developed countries, such as Japan, France, U.S. etc. As a result, we dont have enough critical mass in any theoretical science research field. In order to have research man power in a particular field comparable to, say Tokyo University which has 60 permanent faculties in mathematical science, we actually have to group all the work forces of several universities. NCTS is for such a purpose. Under topical program of NCTS, local mathematicians in the same field are pulled together for going out to various international stages. We can win together. Finally, the Young Theorists Award of NCTS enters its 2nd year, with three mathematicians receiving this award : GuanYu Chen (NCTU), Ming-Yi Lee (NCU), and Jyh-Haur Teh (NCTU). G.-Y. Chen specializes in probability theory and related topics, with degrees from both Cornell U. and NCTU. M.Y. Li is analyst graduated from NCU, and now works also on certain PDE. J.-H. Teh works on algebraic geometry and topology, had his degree from Stony Brook. These recipients were selected by our executive committee basing on evaluation of all the applicants by international experts.

Executive Committee Members Committees Gerard J. Chang

Affiliation National Taiwan University

Chiun-Chuan Chen

National Taiwan University

I-Liang Chen


Wen-Wei Lin

National Chiao Tung University

Yuah-Chung Sheu


Chin-Lung Wang


Soon-Yi Wu

National Cheng Kung University

Jing Yu

National Tsing Hua University

5 ‹‹- Report of the Division Head

Academic Committee Members Committees Jung-Kai Chen

Affiliation National Taiwan University

Shun-Jen Cheng

Academia Sinica

Sze-Bi Hsu

National Tsing-Hua University

Jonq Juang


Yng-Ing Lee


Song-Sun Lin


Tai-Chia Lin


Dong-Ho Tsai


Julie Tzu-Yueh Wang

Academia Sinica

Wei-Cheng Wang


Soon-Yi Wu

National Cheng Kung University

Jing Yu


Xuding Zhu

National Sun Yat-sen University

Executive Committee Members -›› 6

Highlights of the Programs D.1 Algebra Coordinators: Shun-Jen Cheng (Academia Sinica) Meng-Kiat Chuah (National Tsing Hua University)

his research group focuses on various aspects of Lie theory and their related applications. They include Lie superalgebra representations, group representations, vertex operator algebras, finite groups, quantum groups, and related combinatorial structures. Most of the scholars of this topic reside in three major research centers (Academia Sinica, National Tsing Hua University and National Cheng Kung University). They form a close connection and support the activities organized by these centers.

Vyjayanthi Chari (University of California Riverside), Minoru Wakimoto (Kyushu University), Jun Morita (University of Tsukuba), Catharina Stroppel (University of Glasgow), Yun Gao (University of York), Seok-Jin Kang (Seoul National University).

D.1.1 Local Algebra Group (in alphabetical order)

Tainan

Shun-Jen Cheng (AS), Meng-Kiat Chuah (NTHU), Chu-Chin Hu (NTNU), Po Yi Huang (NCKU), Wen Fong Ke (NCKU), Ching Hung Lam (NCKU), Ngau Lam (NCKU), Chufeng Nien (NCKU), Shu-Yen Pan (NTHU), ChianJen Wang (NCTS), Yi-Fan Yang (NCTU).

D.1.2 Visitors Academia Sinica Jae-Hoon Kwon (University of Seoul), Alistair Savage (University of Ottawa), Guanglian Zhang (Shanghai Jiaotung University), Motoko Kotani (Tohoku University), Jie Xiao (Tsinghua University), Jonathan Brundan (University of Oregon), Alexander Kleshchev (University of Oregon), George Lusztig (MIT), Nicolai Reshetikhin (University of California - Berkeley),

Hsinchu Jing-Song Huang (Hong Kong University of Science and Technology), Kyo Nishiyama (Kyoto University), Hiroshi Yamashita (Hokkaido University), Cheng-Bo Zhu (National University of Singapore).

Kyo Nishiyama (Kyoto), Hiroyuki Ochiai (Nagoya), Ruibin Zhang (Sydney), Hiroshi Yamauchi ( Aichi), Gerald Hohn ( Kansas State), Toshiyuki Abe ( Ehime), Hiroki Shimakura (Aichi), Christian E. Lomp (Univ. do Porto), Koichi Betsumiya (Jobu), Robert Griess (Michigan), Gunter Pilz (Linz), Hubert Kiechle (Hamburg).

D.1.3 Seminars A student seminar is held in Academia Sinica approximately 4-6 times every month. Students are given reading assignments and are then asked to present them in class. Sometimes faculty members also give talks in this seminar. Topics include representation theory of the general linear group in characteristic p following Zelevinsky, the classification of TDS of semisimple Lie

7 ‹‹- Highlights of the Programs

algebra following Kostant, the theory of translation functors following Jantzen, representation theory of Yangian following Molev, the determination of the Shapovalov determinant for the generalized Verma modules following Jantzen etc. During July and August 2008, two student seminars are organized at Hsinchu for the NCTS summer interns. Meng-Kiat Chuah runs a student seminar on Lie algebras, and ShuYen Pan runs a student seminar on prime numbers. A regular seminar is run weekly at NCKU: including lectures given by visitors and given by the local group members. The main theme is on the representation theory. The topics include the representations of algebraic groups, Lie super algebras, vertex operator algebras etc. A student seminar is also run by Wen Fong Ke and Ching Hung Lam at weekly basis at Tainan. This seminar primarily aims at graduate students. The main subjects are Young diagrams and representations of symmetric groups in 2007/2008.

D.1.4 Workshops Workshop on Algebraic Aspects of Lie Theory, December 20-23, 2007 in Academia Sinica (sponsored by grants from Academia Sinica) Subject: Recent developments in representation theory, including representations of quantum groups, e.g. the theory of canonical basis and crystal basis, finite W-algebras, Khovanov algebras, and their connections with representation theory of Lie superalgebras. Further topics include representations of affine superalgebras and toroidal algebras and vertex operator algebras. Speakers: Chin-Hung Lam (National ChengKung University), Shu-Yen Pan (National Tsinghua University), Jie Xiao (Tsinghua University), Jonathan Brundan (University of Oregon), Alexander Kleshchev (University of

Highlights of the Programs -›› 8

Oregon), George Lusztig (MIT), Nicolai Reshetikhin (University of California Berkeley), Vyjayanthi Chari (University of California - Riverside), Minoru Wakimoto (Kyushu University), Jun Morita (University of Tsukuba), Catharina Stroppel (University of Glasgow), Yun Gao (University of York), Seok-Jin Kang (Seoul National University)

NCTS Winter Workshop on Representation Theory, January 23-27, 2008 at NCTS (Hsinchu) Subject: Representation theory of Lie groups by four visitors from Hong Kong, Japan and Singapore, as well as topics in Lie theory by four local scholars. Speakers: Shun-Jen Cheng (Academia Sinica), Meng-Kiat Chuah (National Tsing Hua University), Jing-Song Huang (Hong Kong University of Science and Technology), Ching Hung Lam (National Cheng Kung University), Kyo Nishiyama (Kyoto University), Shu-Yen Pan (National Tsing Hua University), Hiroshi Yamashita (Hokkaido University), Cheng-Bo Zhu (National University of Singapore). Organizers: Meng-Kiat Chuah and Jing-Song Huang.

Workshop on Combinatorics and Algebras. July 4-July 7, 2008 at NCKU Subjects: Parking functions, finite calculus, graphs Speakers: Jun Ma, Y-N. Yeh, X. Chu. Organizer: Po Yi Huang

Summer School on Lie Theory at Tainan, Aug. 11-Aug. 19, 2008 Subjects: Representations of Lie groups, Lie super algebras and quantum groups Speakers: Shun-Jen Cheng (Academia Sinica), Meng-Kiat Chuah (NTHU), Kyo Nishiyama (Kyoto), Hiroyuki Ochiai (Nagoya ), Ruibin Zhang (Sydney). Organizer: Ngau Lam

NCTS/Academia Sinica Winter School in Representation Theory in NCTS/ TPE from December 18-December 27, 2008 The winter school is aimed at graduate students and researchers in representation theory and includes two 10-hour lecture series by given Raphael Rouquier (Oxford University) and Shrawan Kumar (University of North Carolina – Chapel Hill).

Lie Theory Workshop in Academia Sinica, from December 28 to December 30, 2008 Subject: Topics include representations theory of Lie superalgebras, Hecke algebras, finite Walgebras, and geometrical and homological methods in representation theory. Further

topics include representations of real Lie groups and vertex operator algebras. Speakers include: Meng-Kiat Chuah (National Tsinghua University), Tomoyuki Arakawa (Nara Women's University, Japan) , Jae-Hoon Kwon (University of Seoul, Korea), Zongzhu Lin (Kansas State University, USA), Masahiko Miyamoto (University of Tsukuba, Japan), Liangang Peng (Sichuan University, China), Alexander Premet (University of Manchester, UK), Raphael Rouquier (Oxford University, UK), Vera Serganova (University of California, Berkeley, USA), Eric Sommers (University of Massachusetts, Amherst, USA), Weiqiang Wang (University of Virginia, USA)

D.2 Algebraic Geometry Coordinators: Hui-Wen Lin (National Taiwan University)

fter the workshop on Higher Dimensional Algebraic Geometry and the summer school on the latest development of higher dimensional Minimal Model Program held in 2007, the year 2008 is a practice year for local algebraic geometry researchers to carry out their works. In this period, although there are no big conferences or workshops on Algebraic Geometry as in the previous years, many local algebraic geometers do make great progresses in their researches through private research seminars and oversea visiting programs. Besides, the weekly student seminar and the summer courses are still designed to provide students enough background for advanced study on the latest development of Algebraic Geometry.

D.2.1 Accomplishments 1. The NCTS frequent visitor Y.-P. Lee at Utah continues his collaboration with H.-W. Lin and C.-L. Wang. They completed the

study of invariance of Gromov-Witten theory under a simple flop during the winter and spring visiting of Y.-P. Lee at NCU. The breakthrough in this work is to achieve the higher genus invariance by combining their prior result on invariance of big quantum cohomology ring with C. Teleman's very recent result on classifications of semi-simple Frobenius structures. Lee, Lin and Wang also found a complete proof to the invariance of quantum rings under a splitting flop which is an ordinary flop with the exceptional set being a splitting projective bundle over the general base. This was done during the summer visiting of Y.-P. Lee at NCTS. The major achievement in this work is to carry out completely a case of ordinary flops with general base. 2. In this period, Jungkai. A. Chen at NTU had visited Chritopher Hacon at University of Utah. Chen and his coworkers study the basket of singularities introduced by M. Reid in a more systematical way and 9 ‹‹- Highlights of the Programs

obtained various results including: (1.) Non-vanishing of plurigenera (resp. antiplurigenera) for three-folds of general type (resp. weak Q-Fano threefolds), (2.) Lower bound of canonical volume (resp. anti-canonical volume) for threefolds of general type (resp. weak Q-Fano threefolds), (3.) Effective birationality of pluricanonical map for threefolds of general type.The breakthrough of his recent work is to describe the relation between flips and "unpacking", which provide another viewpoint to attack the termination problem of flips. 3. The frequent visiting graduate student Chen-Yu Chi at Harvard University and his advisor Professor Shing-Tung Yau, who is also the Chair of NCTS Scientific Advisory Committee, have initiated a new geometric approach to problems in birational geometry recently. By using this new approach, they provided a beautiful analytic criterion for birational equivalence between smooth varieties of general type via checking only one pluricanonical system. Chi announced their results and gave the detailed report in two NCTS Seminars in Algebraic Geometry in June 2008. 4. The center scientist J.-C. Chen visited Kawakita at RIMS, Fujino at Nagoya University, Jason Starr at Stony Brook, Lawrence Ein and Mihnea Popa at University of Illinois. His current results are the following: (1.) If a variety X has only quotient singularities and the pseudo index i > n/2 +1, then Pic(X) = 1. (2.) Let X be a 3-dimensional smooth Deligne-Mumford stack. Chen and his coauthor H.-H. Tseng constructed a moduli space and proved that it is a crepant resolution of the coarse moduli space of X. They are trying to extend this to other moduli spaces associated to X.

D.2.2 Student Programs


1. Student Seminars on MMP There are two weekly based programs toward the MMP: (1) One is organized by C.-L. Wang and H.-W. Lin and held at NCU from February 2008 to June 2008. The main contributors include two students of NCU. Bin-Je Hung reported the construction of Hilbert scheme and Mori's theorem on the existence of rational curves by using the Bend and Break technique. Jian-Nan Yang reported some fundamental materials in complex geometry. (2) The other one is organized by J.-C. Chen and held at NCTS from September 2007 to June 2008. The main contributors include three NCTS research assistants Chih-Chi Chou, Sung Yih and Wei-Liang Liu. During the fall of 2007 they reported on fundamental material in algebraic geometry as in Hartshorne's text. In the spring of 2008 they reported on the book by Kollar and Mori on birational algebraic geometry, especially on the MMP.

2. Student Seminars on Complex Geometry It is a weekly based program organized by C.-L. Wang and held at NCTS from March to July 2008. The main contributors include three NCTS research assistants Chih-Chi Chou, Sung Yih and Wei-Liang Liu. The major focus is on Hormander's book on complex manifolds, especially on the L2 estimate of dbar equation. They end up with an introduction to the multiplier ideal sheaves and the proof of Nadel's vanishing theorem.

3. NCTS Summer School on Algebra and Algebraic Geometry It is organized by Jyh-Haur Teh from 2008/6/30 to 2008/8/31. This course is designed for freshmen and sophomores. The main texts are Abstract algebra by Ash and Elementary geometry of algebraic curves by Gibson. In the first month they run through groups, rings and fields. In the second month, they study some fundamental facts of algebraic curves.

D.3 Differential Geometry & Geometric Analysis Coordinators: Chiung-Jue Sung (National Tsing Hua University)

he subject matter of Riemannian geometry has multiple faucets. NCTS has held various programs and workshops in related subject areas since the year 2004, focusing on various aspects of geometry and geometric analysis. The covered topics include Conformal Geometry, Special Lagrangian Submanifolds and Mirror Symmetry, Function Theory, Geometric Elliptic and Parabolic Equations, Mathematical Physics, Geometric Evolution Equations, and Mathematical Aspects of General Relativity. The programs and workshops brought together graduate students, recent Ph. Ds and well-established mathematicians, while the short-courses provided necessary background material for the related workshops. The programs and workshops also involved both short and longer term visitors to NCTS.

D.3.1 Advanced Courses and Workshops I. Course / Summer & Winter Programs (I) NCTS & NTHU Joint Course on Singular Integral Operators, Pseudo-differential Operators and Analysis on Homogeneous Groups, May 8 ~ July 28, 2008 Instructor : Prof. Der-Chen Chang (Georgetown Univ. & NCTS) Prof. Chiung-Jue Sung (National Tsing Hua University) Course Description and Requirements: The course is aimed at concisely presenting the basic concepts and principles of Fourier analysis as well as its applications on nilpotent Lie groups, such as Euclidean spaces, Heisenberg groups to graduate or senior undergraduate students in mathematics. It includes some recent results that can be taught at an elementary level and anable students to reach quickly the frontiers of current mathematical research along the direction of

harmonic and geometric analysis. We are going to cover the following topics. 1. The Hilbert transform and the Cauchy integral 2. Homogeneous distributions in Rn 3. Lp theory of singular integral operators (if we have time, we will also cover basic Hp theory) 4. Lp estimates on pseudo-differential operators 5. Parametricies and extimates for elliptic operators 6. Cauchy-Szego integral and the Heisenberg group – 7. The ∂b-complex on the Heisenberg group 8. Geometric mechanics on the Heisenberg group and its generalizations – 9. The ∂-Neumann problem 10. The heat kernel and Riemann zeta function associate to the sub-Laplacian on the unit sphere in Cn. (II) NCTS Summer 2008 Program: Mini Lecture Series and Student Seminar Time: July 4, July 11, July 18, July 24, 2008 PM2:00-4:00 Topic: Introduction to the Maximum Principle for Parabolic Equations Speaker: Prof. Dong-Ho Tsai (NTHU)

II. Workshop: (I) 2008 NCTS Workshop on Harmonic and Complex Analysis, May 19-20, 2008 Organizers: Prof. Der-Chen Chang (Georgetown Univ. & NCTS) Prof. Chiung-Jue Sung (National Tsing Hua University) Invited Speakers: • Methods and techniques for finding heat


kernels, Der-Chen Chang (Georgetown University, USA) • The boundedness of operators on weighted Hardy spaces, Ming-Yi Lee (National Central University) • Module of horizontal vector measures on Carnot groups, Irina Markina (University of Bergen, Norway) • Universal sampling of band-limited signals, Alexander Olevskii (Tel Aviv University, Israel)

Jun-Muk Hwang (KIAS) • Uniqueness and Algebraic Dependence of Holomorphic Curves into Abelian Varieties, Min Ru (University of Houston) • Limit Set of the Harmonic Map Heat Flows, Chiung-Jue Sung (National Tsing Hua University) • Improved Estimate for Lojasiewicz Inequality and Related Results, Wing-Keung To (National Singapore University)

• Operators on Manifolds with Corners, B.Wolfgang Schulze (University Postdam, Germany)

• Evolving a Convex Closed Curve to Another One via a Length-preserving Linear Flow, Dong-Ho Tsai (National Tsing Hua University)

• The inverse of the sub-Laplacian on the weight spaces, Jingzhi Tie (University of Georgia, USA)

• Fake Projective Planes, Geography of Surfaces and Fake Hermitian Symmetric Spaces, Sai Kee Yeung (Purdue University)

• Boundary behaviour of conformal maps and angular derivatives, Alexander Vasil'ev (University of Bergen, Norway)

D.3.2 Seminars

(II) 2008 NCTS Workshop on Geometric Analysis and Several Complex Variables, June 24 & 25, 2008 Organizers: Prof. Der-Chen Chang (Georgetown Univ. & NCTS) Prof. Chiung-Jue Sung (National Tsing Hua University) Invited Speakers: • Finding Heat Kernels Using Geometrical Mechanics, Path Integrals and Other Methods, Ovidiu Calin (Eastern Michigan University) • Geometric Analysis on the Unit Three Sphere, Der-Chen Chang (Georgetown University, USA) • Isolated Complex Singularities and Their CR Links, Xiaojun Huang (Rutgers University) • On Holomorphic Self-Maps of Fano Manifolds with Second Betti Number One,


Speakers include: Ching-Hung Lam (National Cheng Kung University), Hui-Wen Lin (National Central University), Kuo-Chang Chen (National Tsing-Hua University), ChengHsiung Hsu (National Central University), K. Stempak (Politechnika Wroclawska, Poland), Chin-Cheng Lin (National Central University), ( ), Jui-Tang Ray Chen (National Tsing-Hua University), Alexander Vasiliev (Univ. of Bergen), Irina Markina (Univ. of Bergen), Chiung-Ju Liu (National Cheng Kung University), Alexander Olevskii (Tel Aviv University, Israel), B.-Wolfgang Schulze (University Postdam, Germany), Ovidiu Calin (Eastern Michigan University), Duy-Minh Nhieu (San Diego Christian College)

D.3.3 Student Seminars Topics include: On the pseudo-harmonic heat flow, Geometry of Harmonic Maps, The Harmonic Map Heat Flow, The Existence of Blackhole due to Condensation of Matter

D.4 Discrete Mathematics Coordinators: Gerard Jennhwa Chang (National Taiwan University) Xuding Zhu (National Sun Yat-sen University)

D.4.1 Background and activities in the program

iscrete mathematics has seen rapid development in recent decades, both abroad and in Taiwan, in width and in depth. As a focus group of NCTS, the discrete mathematics group has been focused on research in graph coloring, graph labeling, combinatorial optimization, algorithms, enumerative combinatorics, cluster combinatorics, combinatorial number theory. In the past year, through seminars, workshops and hosting visitors, the project has helped local focus group, especially young researchers in the group, to establish collaborations with researchers abroad, develop links with experts abroad, and start their research in the frontier of related fields. Discrete mathematics program in NCTS has two teams, one in north which is organized by Gerad Jennhwa Chang at National Taiwan University, the other in south which is organized by Xuding Zhu at National Sun Yatsen University. Each semester, the discrete mathematics groups in north and south have series of seminars. Some of the seminar talks are given by visitors and some talks from group members, post doctors and students. During the past year, the discrete mathematics group in north has invited 8 visitors. As we do not have budge for post doctors, we use personal NSC projects of Gerard Jennhwa Chang to hire a post doctor, Jiaojiao Wu, joining the program. In the past year, the group in south has invited 4 visitors. Professor Andre Raspaud, Professor Arnaud Pecher and Professor Mickael Montassier from Bordeaux, France

and Professor Pavol Hell from Simon Fraser University, Canada. Professors Raspaud, Pecher and Montassier stayed for two weeks and Professor Hell stayed for one month. Both groups have long time collaborations with our group. During their visits, we initiated some new joint projects. Collaborations continue after their visits. The main focus on the south group is graph colouring. We initiated studies on adapted graph colouring and some other colouring problems. We have written two joint papers based on our joint work during and after their visits. One paper is already accepted by European Journal of Combinatorics, and the other is under revision. The visit also made the arrangement t have a newly graduated Ph.D. to do one year post doc. research in Bordeaux. Some other collaborations with earlier visitors are also working well. Dr. Serguei Norine visited our group in March of 2007. Joint work on consecutive circular list colourings were initiated during the visit. We continue our joint work on this subject after his return. Up to now, members from our group have written three joint papers with him. During this period, our group members also visited other institutions. Li-Da Tong visited Bordeaux for two weeks in 2007, and Xuding Zhu visited University of Victoria for two weeks in 2008, and visited Charles university in Prague for two weeks in the summer of 2008. Joint works initiated during these visits are carried out.

Local focus group North: Gerard Jennhwa Chang (NTU), KoWei Lih (AS), Jing-Ho Yan (Aletheia), HsunWen Chang (Tatung), Chiang Lin (NCU), Hong-Gwa Yeh (NCU), Sheng-Chyang Liaw (NCU), Roger Kwan-Ching Yeh (Feng-Chia), David Kuo (NDHU), post doctors and graduated students.


South: Xuding Zhu (NSYSU), Meng-Na Lo (NSYSU), Tsai-Lien Wong (NSYSU), Li-Da Tong (NSYSU), Mei-Hui Guo (NSYSU), Zhishi Pan (NSYSU), Sen-Peng Eu (NUK), Szu-En Cheng (NUK), Hong-Gwa Yeh (NCU), plus 5 Ph.D. students.

Visitors Khee Meng Koh (National University of Singapore), Frank Kwang-Ming Hwang (National Chiao Tung University), Silvia Heubach (California State University), WenJie He (Hebei University of Technology), KaiShun Wang (Beijing Normal University), WaiHong Chen (Hong Kong Baptist University), Rong-Quan Feng (Peking University), Daphne Liu (California State University, Los Angeles), Wensong Lin (South-East University, Nanjing), Pavol Hell (Simon Fraser University), Andre Raspaud (Laboratoire de Recherche), Arnaud Pecher (Laboratoire de Recherche), Mickael Montassier (LaBRI Laboratoire Bordelais)

Conferences 2007 International Conference on Graph Theory and Combinatorics & Fourth Corssstrait Conference on Graph Theory and Combinatorics (2007.6.24-2007.6.29). Plenary speakers: G. Fan, F. K. Hwang, Y.-N. Yeh, X. Yu, X. Zhu. There are 56 contribution talks.

D.4.2 The accomplishment In the north, publications are listed below. [1] R.-Y. Wu, G.-H. Chen, J.-S. Fu and Gerard J. Chang, Finding cycles in hierarchical hypercube networks, Inform. Process. Letters (accepted). [2] L.-H. Huang and G. J. Chang, L(h, k)labelings of Hamming graphs, Disc. Math. (accepted). [3] G. J. Chang, L.-H. Huang and H.-G. Yeh, On the rank of a cograph, Linear Algebra Appl. 429 (2008) 601-605. [4] H. Lai, G. J. Chang and K.-W. Lih, On fully orientability of 2-degenerate graphs, Inform. Process. Letters 105 (2008) 177181. [5] G. J. Chang, Upper bound on k-tuple


domination numbers of graphs, Europ. J. Combin. 29 (2008) 1333-1336. [6] B.-J. Li and G. J. Chang, Clique coverings and partitions of line graphs, Discrete Math. 308 (2008) 2075-2079. [7] J. S.-T. Juan and G. J. Chang, Adaptive group testing for consecutive positives, Discrete Math. 308 (2008) 1124-1129. [8] G. J. Chang, S.-P. Eu and C.-H. Yeh, On the (n, t)-antipodal Gray codes, Theore. Comput. Sci. 374 (2007) 82-90. [9] J.-J. Chen and G. J. Chang, Distance graphs on R^n with 1-norm, J. Combin. Optimization 14 (2007) 267-274. [10] G.-Y. Chang, G.-H. Chen and G. J. Chang, (t, k)-Diagnosis for matching composition networks under MM* model, IEEE Trans. Computers 56 (2007) 73-79. [11] R.-Y. Wu, G.-H. Chen, Y.-L. Kuo and G. J. Chang, Node-disjoint paths on hierarchical hypercube networks, Inform. Sciences 177 (2007) 4200-4207. As for the south, publications of the local group are as below: [1] D. Yang andX. Zhu, Activation strategy for asymmetric marking games, European Journal of Combinatorics, to appear. [2] T. Wong and X. Zhu, Distinguishing number of group actions, Discrete Mathematics, to appear. [3] H. Chang and X. Zhu, Colouring games on outerplanar graphs and trees, Discrete Mathematics, to appear. [4] M. Montassier, A. Raaaspaud and X. Zhu, Adaptive choosability of graphs and orientations, European Journal of Combinatorics, to appear. [5] A. Guan and X., Zhu, Adaptable choosability of planar graphs with sparse short cycles, submitted. [6] X. Zhu, Bipartite density of triangle-free subcubic graphs, Discrete Applied Mathematics, to appear. [7] X. Zhu, Bipartite subgraphs of triangle-free subcubic graphs, Journal of Combinatorial Theory Ser. B, to appear. [8] S. Norine, T. Wong and X. Zhu, Circular

Choosability via Combinatorial Nullstellensatz, Journal of Graph Theory, to appear. [9] W. Lin, D. Yang and X. Zhu, Circular consecutive choosability of graphs,

Taiwanese Journal of Mathematics, to appear. [10] D. Liu, S. Norine, Z. Pan and X.Zhu, Circular consecutive choosability of kchoosable graphs, submitted.

D.5 Dynamical Systems Coordinators: Kuo-Chang Chen (National Tsing Hua University) Chi-Wen Shih (National Chiao Tung University)

ynamical Systems is a major and active field of research in mathematical science. In the topical program of dynamical systems, we organize related activities to broaden the spectrum of current research in Taiwan, to promote the collaboration with international scholars, and to enhance the training of graduate students. Such activities include weekly seminar, an annual workshop, and several mini courses. We also cooperate with the people in the topical program of mathematical biology and scientific computation on some applications and computational aspects of dynamical systems. These activities are listed in the following.

D.5.1 Dynamical System Seminar: The weekly seminar is primarily organized by Kuo-Chang Chen (National Tsing Hua University) and Min-Chia Li (National Chiao Tung University). About half of them are student seminars given by graduate students, among them there were a series of talks on KAM theory, and a series of talks on calculus of variations. A listing of all the seminar talks are available at: http://www.math.cts.nthu. edu.tw/actnews/actnews.php?class=102

D.5.2 Conference and Workshop: CTS Workshop on Dynamical Systems, May 23 - 25, 2008

Organizers: Kuo-Chang Chen: [email protected] Cheng-Hsiung Hsu: [email protected] Contents: The conference talks consist of two mini courses, with a total of six hours lectures, plus nine invited one-hour talks. Mini courses and two of the one-hour talks were delivered by established scholars overseas, other talks were given by researchers in Taiwan. Topics covered are:

1. Mini Courses: (1). Speacker: Masato Tsujii (Kyushu University) Title: Quasi-Compactness of Transfer Operators for Contact Anosov Flows (2). Speacker: Weishi Liu (Kansas University) Title: Invariant Manifolds and Geometric Singular Perturbations

2. One-Hour Talks: (1). Speaker: Ken Palmer (National Taiwan University) Title: Homoclinic Orbits in Singularly Perturbed Systems (2). Speaker: Shih-Feng Shieh ( National Taiwan Normal University) Title: Horseshoes for Coupled Discrete Nonlinear Schrödinger Equations


(3). Speaker: Yi-Chiuan Chen (Academia Sinica)

(2). Speaker: Wen-Chiao Cheng (Chinese Culture University)

Title: Family of invariant Cantor sets as orbits of differential equations (4). Speaker: Ming-Jiea Lyu (National Chiao Tung University)

Title: Introduction to entropy theory Time: 2007/8/14, 2007/8/16, 10:00-11:30, 13:30-15:00. (3). Speaker: Chang-Yuan Cheng (National Pingtung University of Education)

Title: Continuation of Topological Entropy for Multidimensional Perturbations of Snap-Back Repellers and OneDimensional Maps (5). Speaker: Hyung Ju Hwang (POSTECH, Korea) Title:Recent Results in Kinetic Theory (6). Speaker: Jaeyoung Byeon (POSTECH, Korea) Title: Standing Waves for Nonlinear Schrödinger Equations (7). Speaker: Je-Chiang Tsai ( National Chung Cheng University) Title: Traveling Waves in the Discrete Fast Buffered Bistable System (8). Speaker: Suh-Yuh Yang (National Central University) Title: Global Exponential Synchronization and Coupling Topology (9). Speaker: Jung-Chao Ban ( National Hualien University of Education) Title: The Dimension of Non-Conformal Repeller and Average Conformal Repeller

D.5.3 NCTS Summer Course on Dynamical Systems (1). Speaker: Kuo-Chang Chen (National Tsing-Hua University) Title: Introduction to ergodic theorems. Time: 2007/8/7, 2007/8/9, 10:00-11:30, 13:30-15:00.


Title: Convergence of dynamics: Theory and Applications Time: 2007/8/21, 2007/8/23, 11:00-12:00, 13:30-14:30. (4). Speaker: Shyan-Shiou Chen (National Taiwan Normal University) Title: Introduction to Marotto's chaos and LaSalle's invariant principle. Time: 2007/8/28, 10:00-11:30, 13:3015:00. (5) Speaker: Kuo-Chang Chen (National Tsing-Hua University) Title: Recurrence in dynamical systems, 8 hours lectures Time: 15:00-17:00 on July11, 18, 22, 24, 2008 Abstract: This mini course is a short introduction to the concept of recurrence in dynamical systems. We introduce the Poincaré and Birkhoff recurrence theorems, their generalizations, the concept of ergodic and mixing transformations, and some interesting applications. In particular, we show some applications of the recurrence theorems to the combinatorial number theory, namely the Van der Waerden theorem and the Szemerédi theorem. Some of the topics are briefly outlined in the mini course and details are left to the student seminar.

D.6 Mathematical Biology Coordinator: Sze-Bi Hsu (National Tsing Hua University)

he purpose of the topical program in Mathematical Biology is to promote the interdisciplinary interactions between mathematicians, physicists, computer scientists and biologists. In the past one year, we held two biweekly seminars in Neutral Theory of Biodiversity and in Evolutionary Biology ; two intensive courses in Stochastic Process and Stochastic Differential Equations ; one intensive course in Monotone Dynamical Systems with Applications to ReactionDiffusion Equations and several invited talks. There are stated in the followings.

I. Biweekly seminar in Neutral Theory of Biodiversity and Biogeography, September 28 - November 30, 2007 Organizers: Sze-Bi Hsu (Tsing-Hua University) and Yi-Yun Chen (NCTS) In this seminar we study the book "The Unified Neutral Theory of Biodiversity and Biogeography" by Stephen Hubbell. Neutral Theory is used to explain the biodiversity in the community ecology in recent years. The advantage is that the theory fit many data. We study the following subjects:

We study the following subjects: (i) Fitness Landscapes and sequence spaces (ii) Prisoners of the Dilemma (iii) Games in finite populations (iv) Spatial Games (v) HIV infection (vi) Evolution of Virulence (vii) Evolutionary Dynamics of Cancer

III. An intensive course in Monotone Dynamical Systems with Application to Reaction-Diffusion Equations, December 5, 2007 - Jan. 3, 2008 Organizer : Sze-Bi Hsu (Tsing-Hua University) Speaker : Professor Jifa Jiang (Tongi University, Shanghai, PRC) Professor Jiang gave two hours weekly lectures on his work on Monotone Dynamical Systems with Application to ReactionDiffusion Equations and Mathematical Biology.

(i) Dynamical Models of the Relative Abundance of Species,

IV. An intensive course in Stochastic Process and Stochastic Differential Equations in Mathematical Biology

(ii) Local Community Dynamics under Ecological Drift,

Organizer: Sze-Bi Hsu (Tsing-Hua University)

(iii) Metacommunity Dynamics and the Unified Theory,

Speaker: Professor Linda Allen (Texas Tech. University, USA) Date: Aug. 5, 7, 12, 14, 2008 AM10:00-12:00

(iv) The Unified Theory and Dynamical Species-Area Relationship.

Part I: Discrete-Time Markov Chains - DTMC

II. Biweekly seminar in Evolutionary Dynamics, Feb. 29 - May 30, 2008

• Theory • Applications to Random Populations, and Epidemics Part II: Branching Processes

Organizers: Sze-Bi Hsu (Tsing-Hua University) and Yi-Yun Chen (NCTS) In this seminar we study the book "Evolutionary Dynamics" by Martin Nowak.

Walks,

• Theory • Applications to Cellular Processes, Network Theory, and Populations


Part III: Continuous-Time Markov Chains CTMC • Theory • Applications to Populations and Epidemics Part IV: Stochastic Differential Equations SDE • Comparisons to Other Stochastic Processes, DTMC and CTMC • Applications to Populations and Epidemics

V. An intensive course in modeling techniques and numerical methods for Stochastic Differential equations. Organizer: Sze-Bi Hsu (Tsing-Hua University) Speaker: Professor Edward Allen (Texas Tech. University) Date: Aug. 5, 7, 12, 14, 2008 PM2:00-4:00 Part I: Random variables and stochastic processes are reviewed and stochastic integrals are introduced. Part II: The theory and approximation of Itˆo stochastic differential equations (SDEs) are studied.

Part III: A procedure is explained for deriving accurate SDE models. SDEs are derived for several problems in biology, physics, and finance. Part IV: The derivation procedure is extended to stochastic partial differential equations (SPDEs). SPDEs are derived for several problems in physics and biology.

VI. Several invited talks (i) Topics:The Interface of Developmental Cell Biology and Mathematical Modeling, Nov. 1, 2007 Speaker: Prof. Jui-Chou Hsu (Life Science, NTHU) (ii) Topics: Protein Wrapping: An insight into watertied molecular design, June 16, 2008 Speaker: Professor Ariel Fernandez, Rice University, USA (iii) Topics: Anatomically Accurate Modeling in Cardiac Electrophysiology, July 23, 2008 Speaker: Professor A.V.Panfilov, Utrecht University

D.7 Number Theory Coordinators: Jing Yu (NTHU & NCTS) and J. Tze-Yue Wang (Academia Sinica)

umber Theory at NCTS is understood in a broad sense, including traditional algebraic number theory, arithmetic geometry and automorphic representations.

Diophantine approximations

Diophantine geometry and arithmetic of algebraic function fields are also among the main interests.

Representation of p-adic groups

Main Research Focus of the working group


Diophantine geometry Modular curves Transcendence characteristic

theory

in

positive

D.7.1 Local focus group J. Yu (NCTS Center Scientist and NTHU),

C.-Y. Chang (Post doc), Y.-M. J. Chen (NCU), W.-C. Chi (NTNU), L.-C. Hsia (NCU), A. Li (Fu Jen U.), S.-Y. Pan (NTHU), A. Schweizer (NCTS), C.-J. Wang (Post Doc), J. T.-Y. Wang (Academia Sinica), W.-C. Yao (TMUE), Y. Yang (NCTU), C.-F. Yu (Academia Sinica), Y.J. Yu (Post Doc). Presently there are also 15 Ph.D. students in this group, from NTHU, NCU, and NCTU. The short term visitors this year are : Min Ru (U. Houston), J. Tilouine (U. Paris Nord).

D.7.2 Seminars and Courses NCTS Number Theory Seminar This is regular weekly number theory seminar during the academic year. It includes talks given by visitors to Taiwan from abroad and reports on research results obtained by number theory group at NCTS.

Course on Abelian Varieties This Fall 2008 course is given by Jing Yu. Contents : elliptic curves, Abelian varieties, theorems of the cube and the square, dual abelian varieties, polarizations, Rosati involution, Riemann forms, Poincare divisors, theta divisors, Jacobian.

Course on Function Field Arithmetic Another 2008 Fall course given by A. Schweizer. Content: Riemann-Roch the-orem, -functions, Drinfeld modules, cyclotomic function fields, analogy between number fields and function fields.

NCTS Student's Seminar on Algebra and Number Theory This seminar during academic year aims at Ph.D. students, with students from NTHU, NCU and NCTU join. Sometimes it is proceeded using video conference facilities among these universities. Topics discussed including transcendence problems, Diophantine problems, complex multiplications, etc.

D.7.3 Advanced Schools and Workshops

Winter School on Number Theory and Arithmetic Geometry at Aspire Park Feb. 12-Feb. 15, 2008. Subject: Motives, l-adic representations, Class Field Theory, Algebraic Inde pendence Measures. Speakers: Jing Yu (NCTS & NTHU), Hui-Wen Lin (NCU), Wen-Chen Chi (NTNU), Chieh-Yu Chang (NCTS) and graduate students.

Summer School on Algebra and Number Theory at Aspire Park, June 24-June 28, 2008 Subject: Chow Forms, Diophantine Geometry, Geometric Invariant Theory, Deformations of Galois Representations, Representations of Semisimple groups. Speakers: Jing Yu (NCTS & NTHU), Min Ru (U. Houston), J. Tze-Yue Wang (Academia Sinica), Ment-Kiat Chuah (NTHU), Yih-Jeng Yu (Academia Sinica) and graduate students.

D.7.4 Summer Program for Students The 2008 summer program on algebra is organized by Jing Yu, Shu-Yen Pan and JyhHaur Teh. Topics include prime numbers, algebraic curves, simple algebras over local and global fields (reciprocity, HasseMinkowski principle, and Hilbert symbols), and de Rham cohomology.

D.7.5 Accomplishments [1] T. T. H. An, W. Cherry and J. T.-Y. Wang, Algebraic degeneracy of nonArchimedean analytic maps, preprint 2008. [2] T. T. H. An, J. T.-Y. Wang and P. Wong, Non-archimedean analytic curves in the complements of divisors, Journal of Number Theory 128 (2008), 22752281. [3] C.-Y. Chang, A note on a refined version of Anderson-Brownawell-Papanikolas criterion, to appear in Journal of Number Theory, 2008. [4] C.-Y. Chang and M. Papanikolas, Algebraic relations among periods and loga-rithms of rank 2 Drinfeld modules, preprint 2008.


[5] C.-Y. Chang, M. Papanikolas, D. Thakur and J. Yu, Algebraic independence of arithmetic gamma values and Carlitz zeta values, preprint 2008. [6] C.-Y. Chang, M. Papanikolas and Yu, Frobenius difference equations and algebraic independence of equal characteristic zeta values, preprint 2008. [7] Y.-H. Chen, Y. Yang and N. Yui, Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds, J. reine angew. Math. 616 (2008), 167-203. [8] Y.-M. Chen and J. Yu, On class number relations in characteristic two, Math. Zeit. 259 2008, 197-216. [9] Y.-M. Chen, Averaging class numbers in characteristic 2, to appear in Journal of Number Theory, 2008. [10] S. Fukurara and Y. Yang, Period polynomials and explicit formulas for Hecke operators on Γ 0(2), to appear in Math. Proc. Cambridge Philosophical Society. [11] L.-C. Hsia, On the reduction of a nontorsion point of a Drinfeld module, to appear in Journal of Number Theory, 2008. [12] L.-C. Hsia and J. Silverman, On a dynamic Brauer-Manin obstruction, preprint 2008. [13] M.-H. Kang, W.-C. Li and C.-J. Wang, The zeta functions of complexes from PGL(3) : a representation theoretic approach, preprint 2008. [14] S.-Y. Pan, L-functoriality for local theta correspondences with unipotent reduction for unitary groups, preprint 2008. [15] S.-Y. Pan, L-functoriality for local theta correspondences with unipotent reduction for symplectic and even orthogonal groups, preprint 2008. [16] M. Papanikolas, Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms, Invent. Math. 171 (2008), 123174. [17] Fu-Tsun Wei and J. Yu, On the independence of Heegner points associated to distinct quadratic imaginary


fields in the function field case, preprint 2008. [18] Y. Yang, Modular Units and cuspidal divisor class groups of X 1(N), preprint 2008. [19] Y. Yang and J.-D. Yu, Structure of the cuspidal rational torsion subgroup of J1(pn), preprint 2008. [20] Y. Yang and W. Zudilin, An Sp4 modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds, preprint 2008.

D.7.6 Exchange programs and international cooperations Besides individual visits by members of our focus group to centers and universities in Canada, China, France, Germany, Hongkong, Japan, Korea, U.S.A., highlights of 2008 international cooperations include : Canada. July 2008 J. Yu was invited to CNTA conference at Waterloo University, together with C.-Y. Chang and 3 students. This conference was held immediately after the Fields Institute Summer School which these students enrolled in. Fall 2008, L.-C. Hsia, J. T.-Y. Wang and J. Yu are also invited to the Fields Institute program on Arithmetic Geometry and Hyperbolic Geometry. In Fall 2007, Y. Yang visited Queens University, with his student Y.-H. Chen, and collaborated with N, Yui on arithmetic of Picard-Fuch equations. France. July 2008, L.-C. Hsia visited Luminy center for one month (research in pairs program), works on arithmetic Dynamics. Germany. Spring 2008, Y. Yang visited MaxPlanck Institute in Bonn, with his student Y.-H. Chen (supported by NCTS). Japan. October 2007, Jing Yu and his student F.-T. Wei were invited to conference on Galois theory and related topics at Yamagata. Korea. Jan. 2008, J. Yu, L.-C. Hsia, Y.-J. Yu, Y. Yang, K.-S. Tan were invited to KAIST, joining East Asian Number Theory Conference as invited speakers. USA. Jan. 2008, L.-C. Hsia was invited to AIM workshop on arithmetic dynamics. March

2008, J. Yu was invited to Arizona Winter school AWS as NSF observer. C.-Y. Chang was invited as post doctor assisting that school. Later on Chang visited Texas A & M University cooperating with M. Papanikolas on transcendence theory in positive characteristic.

D.7.7 Student's activities and schools Since 2004 each year we have one week winter school and one week summer school on various topics in number theory for graduate students, sponsored by Minister of Education grant (national chair in science) and NCTS, usually this is taken place at a conference site outside NCTS.

We have also supported travels of Ph.D. students to join selected summer/winter schools, or workshops abroad in 2008 : 1 student to the Arizona arithmetic geometry winter school taking part in its student project, 1 post doctor and 1 student to the annual algebraic number theory workshop at Waseda University, 3 students to the Fields institute summer school. There is 1 student joining Fall program (3 months) of the Fields Institute. All these students applied (and received) local support from the organizers of these international organizations.

D.8 Partial Differential Equations Coordinators: Chiun-Chuan Chen, Tai-Chia Lin, Jenn-Nan Wang (National Taiwan University), Jong-Shenq Guo (National Taiwan Normal University)

D.8.1 Background and activities in the program he activities Nonlinear PDE at NCTSTPE in the program include regular PDE seminars, courses, workshops/ conferences, and international cooperation.

Local focus group : Jong-Shenq Guo (NTNU), I-Liang Chern (NTU), Chang-Shou Lin (NTU), Chiun-Chuan Chen (NTU), Tai-Chia Lin (NTU), Jenn-Nan Wang (NTU), Chun-Chi Lin (NTNU), HueyEr Lin (NTNU), Jenn-Long Chern (NCU), JeChiang Tsai (CCU), Sheng-Chen Fu (NCCU), Mao-Sheng Chang (Fujen U), Chung-Tsun Shieh (Tamkang U), Dong-Ho Tsai (NTHU), Chi-Kun Lin (NCTU), Chao-Nien Chen (NCUE), Chun-Kong Law (NSYSU), ChingLung Lin (NCKU)

Short Term Visitors: Yoshihito Oshita, Yokihiro Seki, Ken-Ichi Nakamura, Yoshihito Morita, Hirokazu Ninomiya, Gen Nakamura, Yoshihiro Tonegawa, Reika Fukuizumi (Japan), Dongho Chae, Hyeonbae Kang, Namkwon Kim (Korea), Juncheng Wei (HongKong), Philipppe Souplet (France), Gunther Uhlmann (USA), Gennady El (United Kingdom), Anatoly Mikhajlovich Kamchatnov (Russia).

Courses • Basic theory of ODEs and its applications, July 16-August 22, 2008, organized by JongShenq Guo: This summer course has been organized twice. In the first three weeks, basic theory of ODE such as existence and uniqueness theory for IVP, theory of continuation of solution, continuous dependence on initial value and/or parameter, comparison principle, shooting, etc are introduced. Also, some recent results on


traveling waves are given. These lectures are given by Professors S.-C. Fu (NCCU), J-C. Tsai (CCU), and C.-C. Wu (NCTU). In the fourth week, some special solutions, such as stationary solution, self-similar solution, traveling wave solution, spiral wave solution, etc, of some PDE problems are introduced by Guo. There are 10 students selected. 3 of them are to be senior and 6 are to be first year in graduate program of NTU, and 1 is to be in NCTU. In the final two weeks, these students are assigned some papers related to some special solutions of PDE to read and present. This year, these students are quite excellent. • Minicourse on Inverse Problems, March 19-21, 2008, NTU, organized by Jenn-Nan Wang. This minicourse were given by three prominent mathematicians in the field of inverse problems. Professor Hyeonbae Kang (Korea), Small Volume Imaging Professor Gen Nakmura (Japan), Reconstruction methods for inverse problems Professor Gunther Uhlmann (USA), Invisibility

Conferences and Workshops • France-Taiwan Joint Conference on Nonlinear PDEs, March 25-28, 2008 at CIRM, Marseille, France. Organizers: Thierry Gallay, Jong-Shenq Guo, Francois Hamel, Jean-Michel Roquejoffre Speakers: Jung-Chao Ban, Chiao-Nien Chen, Kuo-Chang Chen, Jong-Shenq Guo, John Meng-Kai Hong, Sze-Bi Hsu, Chang-Shou Lin, Chun-Chi Lin, Jenn-Nan Wang from Taiwan. Guy Barles, Karine Beauchard, Henri Berestycki, Yann Brenier, Didier Bresch, Anne de Bouard, Albert Fathi, Isabelle Gallagher, Michel Ledoux, Emmanuel Russ, Laure Saint-Raymond, Eric Sere from France. • Workshop of Dispersive PDE and Integrable Systems, March 28, 2008, at NTU. Organizers: Tai-Chia Lin, Jyh-Hao Lee Speakers: Leonid V. Bogdanov (Seniour


researcher of L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Russia), Oleg I. Mokhov (Centre for Nonlinear Studies, Landau Institute for Theoretical Physics, Russian Academy of Sciences, Russia), Tsarev Sergey, Krasnoyarsk State Pedagogical University, Russia), Anatoly Mikhajlovich Kamchatnov (Principal Researcher and Deputy-head of Theoretical Department, Institute of Spectroscopy, Russian Academy of Sciences, Troitsk, Moscow Reg., Russia), Gennady El (Department of Mathematical Sciences, Loughborough University, United Kingdom), ( ) • Workshop of Nonlinear Partial Differential Equations Related to Physical Models, May 30-31, 2008, organized by TaiChia Lin. Speakers: Jun-cheng Wei (Chinese University of Hong Kong), Liping Wang (Chinese University of Hong Kong), Wei Yao (Chinese University of Hong Kong), Yoshihisa Morita (Ryukoku University), Yoshihiro Tonegawa ( Hokkaido University), Reika Fukuizumi (Hokkaido University), Namkwon Kim (Chosun University), Dongho Chae (University of Chicago), Shusen Yan (The University of New England), Je-Chiang Tsai (ational Chung Cheng University)

D.8.2 The accomplished and the anticipations Selected publications of the local focus group during 2008: [1] Chiun-Chuan Chen, Robert M. Strain, Horng-Tzer Yau, and Tai-Peng Tsai, Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations, Int. Math. Res. Notices (2008) Vol. 2008, article ID rnn016, 31 pages. [2] Chiun-Chuan Chen and Chang-Shou Lin, Topological degree of a Liouville type equation with singular source, 2008. [3] Jong-Shenq Guo and Bei Hu, Blowup rate estimates for the heat equation with a

[4]

[5]

[6]

[7]

[8]

nonlinear gradient source term, Discrete and Continuous Dynamical Systems 20 (2008), 927-937. Xinfu Chen, Jong-Shenq Guo, and ChinChin Wu, Traveling waves in discrete periodic media for bistable dynamics, Archive Rational Mech. Anal. 189 (2008), 189-236. Gunther Uhlmann and Jenn-Nan Wang, Reconstructing discontinuities using complex geometrical optics solutions, SIAM J. Appl. Math., Vol 68 (2008), 1026-1044. Horst Heck, Xiaosheng Li, and Jenn-Nan Wang, Identification of viscosity in an incompressible fluid, Indiana Univ. Math. J., Vol 56 (2007), 2489-2510. Chiun-Chang Lee and Tai-Chia Lin, Incompressible and compressible limits of two-component Gross-Pitaevskii equations with rotating fields and trap potentials, J. Math. Phys. 49, 043517 (2008). Lin, T.-C. and Wei, J., Orbital stability of bound states of semiclassical nonlinear Schrodinger equations with critical nonlinearity, SIAM J.Math.Anal. Vol. 40 No.1 (2008) 365-381.

In [1], C.C. Chen, R. Strain, H.T. Yau and T.P. Tsai studied the regularity of axisymmetric incompressible Navier-Stokes equations. The incompressible Navier-Stokes equations are one of the most basic and important systems in describing the behavior of fluid. The regularity of existence of solutions of these equations in two dimensions has been solved while this problem in three dimensions still remains as a big challenge. The axi-symmetric case of the Navier-Stokes equations can be considered as a two dimensional problem with possible singularities on the axis of symmetry, and is under extensive studies among other problems. This research proved that a solution of the axisymmetric incompressible Navier-Stokes Equations cannot blow up if it is bounded by a self-similar scaling proposed by Leray. This result "Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations" has

been published in a top-ranked journal, Int. Math. Res. Notices. In [2], C.-C. Chen and C.-S. Lin studied a Liouville type equation arises from prescribing Gauss curvature problem, the mean field limit of vortices in Euler flows, chemotaxis models in bioscience, and Chern-Simons-Higgs models. In recent years, the study on the Liouville type equation has reached another stage with efforts of many well-known mathematicians. Ding-Yost-Li-Wang and Tarantello-Struwe applied mini-max methods to prove the existence of solutions when the total mass is in some range between 8π and 16π. Walensky-Wang-Wei and PrajapatTarantello classified the ground state solutions for the single-equation case with singular data. Chen-Lin calculated the Leray-Schauder degree of solutions. Wang and Jost studied the blowing-up behavior and classified the ground state solutions for the Toda system. Much of these work relied on the careful study of the phenomenon of energy concentration. The limiting case of the Chern-Simons model proposed by Hong, Kim and Pac can be described by the Liouville type equation with delta functions in the source term. These delta functions make the study of the equation much more difficult. In [3], Chen-Lin obtained an explicit degree formula through combinatorical methods for this case. This degree formula will have many applications, including the proofs of the existence of the Bogomol'nyi system in the electroweak theory of Glashow-SalamWeinberg and the existence of the Toda system of Liouville type equations. In [3], J.-S. Guo and B. Hu studied an initial boundary value problem for the heat equation with a nonlinear gradient source term. It was shown that the blowup rate will never match that of the self-similar variables. In the one space dimensional case with assumptions on the initial data so that the solution is monotonically increasing in time, the exact blowup rate is found. This answer an open problem proposed in the second Euro-Japanese conference on blow-up in Spain in 2006. In [4], X. Chen, J.-S. Guo, C.-C. Wu studied the traveling fronts in discrete periodic


media with bistable nonlinearity. We show that nonzero-speed traveling fronts are unique up to a time translation and are globally exponentially stable. The main tools used to prove the uniqueness and asymptotic stability of traveling fronts are the comparison principle, spectrum analysis, and constructions of super/subsolutions. To prove the existence of traveling fronts, the system is converted to an integral equation which is common in the study of monostable dynamics but quite rare in the study of bistable dynamics. The main difficulty here is the lack of spatial (grid) translation invariance. Introducing a transformation with moving coordinates, we have introduced in this paper a general framework for the study of traveling fronts in discrete periodic media. In [5], in this paper we provide a framework for constructing general complex geometrical optics solutions for several systems of two variables that can be reduced to a system with the Laplacian as the leading order term. We apply these special solutions to the problem of reconstructing inclusions inside of a domain filled with known conductivity from local boundary measurements. Computational results demonstrate the versatility of these solutions to determine electrical inclusions. In [6], in this work we prove a global identifiability of the viscosity parameter in an incompressible fluid by boundary


measurements. In [7], we study the incompressible limit of two-component systems of GPEs with initial data having a large number of vortices and an interface. The incompressible limit may provide the relaxation of turbulence such that the turbulent flow can be self-organized into vortex crystals. Recently, a rich variety of dynamical phenomena ranging from shockwave formation to anisotropic sound propagation has been observed in rotating BECs. To see the dynamical phenomena of rotating two-component BECs, we study the compressible limit of two-component systems of GPEs. The compressible limit may describe geostrophic flow and provide rich dynamical phenomena in rotating twocomponent BECs. In [8], we consider the orbital stability of single-spike bound states of semiclassical nonlinear Schrodinger equations with critical nonlinearity and a trap potential. Due to the effect of the trap potential, we derive the asymptotic expansion formulas and obtain the necessary conditions for orbital stability and instability of single-spike bound states. Our argument is applied to two-component systems of nonlinear Schrodinger equations with a common trap potential, cubic nonlinearity in two spatial dimensions. The orbital stability of bound states with spikes of these systems is investigated. Our results show the existence of stable spikes in two-dimensional Bose-Einstein condensates.

D.9 Probability Theory Coordinator: Yuan-Chung Sheu (National Chiao Tung University)

D.9.1 Quantitative Studies for Markov Processes he qualitative behavior of Markov processes has been analyzed in many aspects and the stability of time homogeneous processes as time tends to infinity has been discovered for many decades. This observation makes it possible to compute the average of a function under a probability measure using Markov processes. Such a method, which is named as Markov chain Monte Carlo (or briefly MCMC), has wide applications in many other disciplines including statistic physics, computer science, biology and etc. In statistic physics, it is common to have to estimate the average configuration or entropy of a dynamical mechanism. In biology, the question could concern the position of the last common ancestor of two related species in the history of evolution or the expected spatial structure of a protein. From the perspective of the MCMC method, this is achieved by simulating a Markov process with desired limiting distribution and choosing the state at a certain time T as a random sample. However, knowing the qualitative behavior of convergence is not sufficient to determine the sampling time T. A quantitative understanding of the mixing time is essential for theoretical results. In practice, various heuristics are used to choose T. Professor Guan-Yu Chen(AM, NCTU) has worked with Laurent Saloff-Coste(Cornell University) on the exploration of the cutoff phenomenon for families of Markov processes since 2003. Recently, during his visit to Cornell University, Guan-Yu Chen and his host Laurent Saloff-Coste discussed the L^2-cutoff for families of reversible Markov processes. They obtained a spectral representation for the L2-mixing time using spectral decomposition

and deduced an equivalent condition on the existence of L2-cutoffs . For an illustration, they applied their method to the family of Ehrenfest chains and obtained a simple condition on the L^2-cutoff and an explicit formula for the L^2-mixing time. This reveals a possibility on the determination of the L^2cutoff for Markov chains with orthogonal polynomials as the eigenvectors. Moreover, they studied the relationship between the first and the second non-trivial eigenvectors and acquired a sufficient condition on the total variation cutoff.

D.9.2 Branching Processes and its Ramifications Branching processes in discrete time, also called Galton-Watson processes, first appeared as a discrete-time stochastic process to model the extinction of British peerage. Its continuous-state and continuous-time generalization has received attentions ever since the first half of 20th century. In order to capture the number of offspring in each generation and to record the positions of the individuals, one considers a measure-valued process. A superprocess is a continuous limit of such measure-valued processes and it has been studied extensively since the end of the eighties. Important researchers in this area include Watanabe, Dynkin, Dawson , Le Gall and others. While its theory is intriguing in itself, it also plays an important role in the study of, for example, nonlinear partial differential equations and that of fractal geometry. The idea to study the genealogical structures of branching processes by random tress is to construct a probability measure on the set of all the genealogical trees. While the construction of discrete random tree is apparent, it is not the same case for continuous random trees until the sequence of seminal


papers by Aldous. A Brownian snake is a pathvalued process which combines the genealogical structure of the continuous random trees with spatial random motions. It turns out that the Brownian snake is a powerful tool in the study of super-Brownian motion. On the other hand, some recent study also showed the possibility of applications of continuous random trees to many other fields (stochastic coalescence and fragmentation processes, statistical mechanics, combinatorics, to name just a few.) From Dec.26, 2007 to Jan.10, 2008, Professor Jean-Fran\c{c}ois Delmas (CERMICS, Univ.Paris-EST) visited NCTS and gave a series of talks in NCTS, NCTU and Academia Sinica. The research work of Professor Delmas encompasses the aforementioned perspectives of branching processes. In the first talk in Academia Sinica he demonstrated the fragmentation processes associated with continuous random trees and how, as in his recent work, to take into account the notion of mutation in the genealogy of random trees by pruning random trees. In the remaining talks in NCTU and NCTS, he introduced the idea of coalescent processes and detection of cellular aging. His recent work in coalescence is related to the length of coalescent time, that is the time to find two most common recent ancestors of two individuals on the tree, and its asymptotic behavior when the family size tends to infinity.

D.9.3 Probability with Biological Applications The foundation of scientific applications of probability and statistics is the main theme for a series of studies in this focus group. Between 2004 and 2007, we had focused on the studies of graphical models. The mathematical structure of network and pathway analysis (which is one of the most challenging problems in the era of functional genomics) is related to graphic models and their probabilistic properties. The theoretic properties for reconstruction of regulatory networks have been explored by the perspectives of probability and statistics. During the past year, we investigated the


regulatory networks of yeast as a model for eukaryotic cells. These researches are conducted with the collaborations with WenHsiung Li at the University of Chicago, Lei Li at the University of South California, HuaiKuang Tsai, Jengnan Tzeng, and others at Acdemia Sinica.

(I) Summer Course on Probabilistic and Statistic Methods in Bioinformatics (Every Tuesday, July 5 - July 26, 2007, 10:00 - 12:00 and 13:00 - 15:00) This short course introduced the basic techniques of probabilistic and statistic methods in bioinformatics. These techniques will provide the foundation of advanced studied of bioinformatics in the post-genomics era. The course ended with special lectures given by Professor Wen-Hsiung Li (GRC, AS, and the University of Chicago.) Topics: 1. The analysis of one DNA sequence (Prof. Chung-Chin Lu, EE, NTHU) 2. The analysis of multiple DNA or protein sequence( Prof. Wen-Ping Hsieh, IS, NTHU) 3. Blast (Prof. Henry Horng-Shing Lu, IS, NCTU) 4. Gene expression, microarrays, and multiple testing (Prof. Wun-Yi Shu, IS, NTHU) 5. Evolution models (Dr. Yun-Huei Tzeng, GRC, AS) 6. Phylogenetic tree estimation (Dr. Yun-Huei Tzeng, GRC, AS)

(II) Student's seminars and courses Starting from the summer studies in 2008, we will start the on-going investigation of systems biology and bioinformatics. In summer, we will introduce and review research topics related to systems biology and bioinformatics based on the references in literature. These studies will provide the foundation for advanced studies of systems biology and bioinformatics in the postgenomic era that will be addressed by researchers in this field. Also we will continue

the group studies at NCTS to the coming semesters and years. There will be more academic activities held by this study group at NCTS that include seminars, workshops and summer courses. Moreover, there will be support courses in future semesters for students to learn. For instance, Professor BorSen Chen will teach a course of system biology at NTHU in the fall semester, 2008. Professor Yuan-Chung Sheu will teach a course of stochastic control and Professor Henry Horng-Shing Lu will teach a course of statistical learning at NCTU in the fall semester, 2008.

D.9.4 Workshop on Stochastics and Finance (April 21, 2008) This workshop was organized by Prof. Chuan-Hsiang Han(NTHU), Prof. Yuan-Chung Sheu(NCTU) and Prof. Ching-Tang Wu (NCTU).

(1) Prof. Szu-Lang Liao( On the Valuation of CDO and Subprime Financial Crisis (2) Dr. Hongbing Su( ) Pricing and Risk-Managing Libor Exotics in Practice (3) Prof. Cheng-Der Fuh ( / ) The Pricing of Risk and Sentiment: A Study of Executive Stock Options (4) Prof. Chii-Ruey Hwang( ) An Empirical Invariance of Stock Price and Related Problems (5) Prof. Jun Sekine (Institute of Economic Research, Kyoto University , Japan) On Risk-Premium Process in An Equilibrium

D.10 Scientific Computation Coordinator: I-Liang Chern (National Taiwan University)

D.10.1 Background and Description

he rapid growth of high performance computers has transformed the methodology of scientific investigation. Computing is nowadays joined experiment and theory as one of the fundamental tools of investigation. It is safe and cheap. Further, in many cases, it can go beyond experiments or observation, as those in astrophysics or meteorology, etc. The development of computational science needs integration of researchers from different disciplines: mathematics, physics, chemistry, biology, geoscience, engineering, computer

science, etc. The funding of NCTS provided opportunities to bring researchers from different disciplines together. In the year 2007/8-2008/7, we focus on three interdisciplinary topics: (1) core algorithms, (2) computational fluid dynamics, and (3) computational nano-optics. Core algorithm focuses on interface problems, especially on computing surface plasmon polariton appeared in nano-optics. We also introduce multiscale computational methods by organizing short courses. Computational fluid dynamics focuese on CFD code implementation on PC-cluster, multi-grid and multi-level, preconditioner designs for flow solver. Application of CFD technique to computational medicine and industrial


problems. Nano-optics focuses on investigating the topics of optical responses in nanometer scale and the resultant intriguing phenomena such as surface plasmon resonances, plasmonic band gaps, and anomalous light propagation in meta-materials. Through these programs, we integrate researchers from mathematics, physics and engineering. Regular joint seminars and short courses have been organized. We also held several international workshops on scientific computing to bring international researches and local researchers together.

D.10.2 Local focus group (1) Core algorithms: I-Liang Chern (NTU), Chien-Cheng Chang (Academic Sinica and NTU), Yu-Chen Shu (Academic Sinica), Wei-Chung Wang (NTU) (2) Computational Fluid Dynamics: Tony W. H. Sheu (NTU), K. M. Shyue (NTU), J. Y. Yang (NTU), D. L. Yang (NTU), M. J. Huang (NTU), J. H. Lee (NTU), C. C. Yen (Fu-Jen), S. F. Tsai (NTOC) (3) Computational Nano-optics: Din Ping Tsai (NTU), Pui-Tak Leung (NTU), Railing Chang (NTOU), Hai-Pang Chiang (NTOU), Pi-Gang Luan (NCU), I-Liang Chern (NTU), Guang-Yu Guo (NTU), Shen-Chung Chen (FEC), Yung-Chiang Lan (NCKU), Chien-Cheng Chang (NTU), Ruey-Lin Chern (NTU), Chien Liu Chang (NTU), Yuan Fong Chau (LIT), Tai Huei Wei (NCCU), Wei-Chih Liu (NTNU), JiaHan Li (NTU), Sy-Hann Chen (NCYU), Bing-Hung Chen (NDHU), He-Nan Lin (NTHU), Ru-Shi Liu (NTU), Kuo-Pin Chiu (NTU), Yuan-Hsing Fu (NTU), Chih-Ming Wang (NDHU)

D.10.3 Short Term Visitors 2007/8-2008/7 Richard Y-H Tsai (Univ. of Taxes - Austin), Chiu-Yen Kao (Ohio State Univ.), Olof Runborg (KTH, Sweden), Raymond Chan (Chinese Univ. of Hong Kong), Ping Lin (University of Dundee, UK), B. Wakeham (U. of Southampton, UK), N. Zheludev (U. of Southampton, UK), D. Hewak (U. of


Southampton, UK), K. Macdonald (U. of Southampton, UK), N. Papasimakis (U. of Southampton, UK), R. Bakker (Purdue University, USA), M. Thoreson (Purdue University, USA), Z. X. Shen (Nanyang Technological University, Singapore), A. Fedyanin (Moscow State Univeristy, Russia), V. Panov (Moscow State Univeristy, Russia), X. Zhang (U. of Berkely, USA), T. Tanaka (Riken, Japan), H. Jackson (U. of Cincinnati, USA), P. C. Yeh (U. of California, Santa Barbara, USA).

D.10.4 Seminars, short courses and workshops Regular seminars: There are 47 seminars in 2007/8-2008/7 (1) Biweekly seminar on scientific computing and Applied Mathematics (2) Computation and Simulation Monthly Seminars on Nano-photonics

Short courses (1) France-Taiwan Exchange Program Modeling & Simulations of Physiological flows, by Marc Thiriet. May 27-June 17, 2008 (36-hour course) (2) Short course on image processing: Tutorial, Jan. 2, 2008, I-L Chern, A Unified Tight Frame Approach for Missing Data Recovery in Images, Jan. 3, 4, 2008, Raymond Chan (Chinese University of Hong Kong). (3) Short course on Multi-scale Modeling, Analysis and Simulation for Solid Materials by Ping Lin (University of Dundee, UK), 3/28, 4/1, 2008. (4) Frontier Nano-photonic Workshop, Semiconductor Quantum Dots, Nanowires, and Nanobelts: Optical Imaging of New Nanostructures, by Prof. Howard Jackson (Department of Physics, University of Cincinnati, Cincinnati, Ohio, USA), September 05 (Wed.), 2007. (5) Workshop on Nanophotonics: Numerical Computations and Simulations, MetalDielectric Composite Superlenses, by Mark

Thoreson (Photonics and Spectroscopy Lab, Purdue University, USA). Optical nanoantennae: Initial design and characterization with an eye towards device development, by Reuben Bakker (Photonics and Spectroscopy Lab, Purdue University, USA). January 04 (Fri.), 2008 at NTU.

Workshops (1) Mini-workshop on strongly nonlinear wave equations, Aug. 6, 2008 Roberto Camassa, University of North Carolina, USA Long Lee, University of Wyoming, USA Juan-Ming Yuan, Providence University, Taiwan (2) Mini-workshop on computations: Jan. 31, 2008

Multiscale

Heterogeneous multiscale methods with application to the wave equation by Olof Runborg (KTH, Sweden) Wavelet-based Numerical Homogenization by Olof Runborg (KTH, Sweden) A Numerical Multiscale Method for Highly Oscillatory ODEs by Richard Tsai, UTAustin. (3) 2007 Taiwan-Japan Joint workshop on Numerical Analysis and Scientific Computation, Nov. 30 (Fri.) to Dec. 2 (Sun.), 2007 Hiroshi Fujiwara (Kyoto University), Yasushi Hataya (Yamaguchi University), Hitoshi Imai (Tokushima University), Yuusuke Iso (Kyoto University), Takayuki Kitamura (Kyoto University), Tatsuyuki Nakaki (Hiroshima University), Yoshimasa Nakamura (Kyoto University), Mitsuhiro T. Nakao (Kyushu University), Yoshihiro Otani (Kyoto University), Shigeru Takata (Kyoto University), Kenji Tomoeda (Osaka Institute of Technology), Yoshitaka Watanabe (Kyushu University), Yu-Chen Shu (Center for Research on Applied Sciences, Academia Sinica, interface problems) Tony Wen-Hann Sheu (Engineering

Science, NTU), I-Liang Chern (Taiwan University), Keh-Ming Shyue (Taiwan University), Weichung Wang (Taiwan University), Tsung-Min Huang (Taiwan Normal University), Ming-Chih Lai (Chiao Tung University), Chin-Tien Wu (Chiao Tung University), Yin-Tzer Shih (Chung-Hsing University), Ren-Chuen Chen (Kaohsiung Normal University) (4) 2007 International Workshop on Modeling & Simulation in Health, Oct. 22-25, 2007 Day 1:Tutorial course Day 2:Theoretical modeling and numerical simulations & Modeling and scientific computing applied to health problems Day 3:Medical image acquisition and processing 3D reconstruction and meshing Day 4:Modeling, simulation and validation (5) Workshop on Nanophotonics: Numerical Computations and Simulations, January 04, 2008 at NTU Metal-Dielectric Composite Superlenses, by Mark Thoreson (Photonics and Spectroscopy Lab, Purdue University, USA) Optical nanoantennae: Initial design and characterization with an eye towards device development, by Reuben Bakker (Photonics and Spectroscopy Lab, Purdue University, USA) (6) The 5th International Workshop on Nanophotonics, December 04, 2007. The content of this course include a broad introduction to the topic of plasmonic nanophotonics. Its aim is to discuss the newly developed metamaterial nanostructures and their future applications to nanophotonics. The theme of this workshop and speakers invited are Prof. Min Gu (Swinburne University of Technology, Australia) "Femtosecond Laser Lights Optical Microscopy", Prof. Ze Xiang Shen (Nanyang Technological University, Singapore) "Femtosecond 29 ‹‹- Highlights of the Programs

Laser Lights Optical Microscopy: Ultrahigh resolution Raman imaging by optically trapped dielectric microsphere", Prof. Heh Nan Lin (National Tsing Hua University, Taiwan) "Metal and Metal Oxide Nanowires for Nanophotonics", Prof. Ming Wen Chu (National Taiwan University, Taiwan) "Probing Bright and Dark Surface Plasmon Modes in Individual and Coupled Au Nanoparticles Using a Fast Electron Beam", Prof. Ta Jen Yen (National Tsing Hua University, Taiwan) "Magnetic and Two-handed metamaterials", Prof. Shi Wei Chu (National Taiwan University, Taiwan) "Molecular structure probed by optical nonlinear scattering" (7) The 6th International Workshop on Nanophotonics, March 11, 2008. The content of this course include a broad introduction to the topic of plasmonic nanophotonics. Its aim is to discuss the newly developed metamaterial nanostructures and their future applications to nanophotonics. The theme of this workshop and speakers invited are Prof. Nikolay Zheludev (University of Southampton, UK) "Coherent MetaMaterials and the Lasing Spaser", Prof. Dan Hewak (University of Southampton, UK) "Through Thick and Thin: Our Work with Chalcogenide Materials, Films and Devices", Prof. Ruey Lin Chern (National Taiwan University, Taiwan) "LC and Surface Plasmon Resonances for Split Ring Structures" Prof. Shangjr (Felix) Gwo (National Tsinghua University, Taiwan) "Nanoparticle-based Plasmonics: Status and Prospects", Prof. Yung Chiang Lan (National Cheng Kung University, Taiwan) "Cavity-Modulated Resonant Tunneling Effects Caused by Surface Plasmon Excitation", Dr. Kevin Macdonald (University of Southampton, UK) "Long Pulse Delays; A Planar Metamaterial Analog of EIT", Dr. Nikitas Papasimakis (University of Southampton, UK) "Nanophotonics Under the Electron Microscope"


D.10.5 Select publications of the local focus group [1] Chern, I-Liang and Yu-Chen Shu, Coupling interface method for elliptic interface problems, Journal of Computational Physics, no. 225 (2007) 2138-2174.(SCI) [2] Chang, C.C., Y-C Shu and I-L. Chern, Solving guided wave modes in plasmonic crystals, Phys, Rev. B, 78, 035133 (2008) (SCI) [3] C. M. Ho, S. F. Tsai, R. K. Lin, P. C. Liang, Tony W. H. Sheu, R. H. Hu, P. H. Lee (2007), Computer simulation of hemodynamic changes after right lobectomy in a liver with intrahepatic portal vein aneurysm, Journal of the Formosan Medical Association, Vol. 106, issue 8, pp. 617-623 (SCI) [4] Tony W. H. Sheu, V. C. Huang (2008), Development of an electro-osmotic flow model to study the dynamic behavior in human meridian, International Journal for Numerical Methods in Fluids, Vol. 56, pp. 739-751 (SCI) [5] Tony W. H. Sheu, H. F. Ting, R. K. Lin (2008), An immersed boundary method for the incompressible Navier-Stokes equations in complex geometry, International Journal for Numerical Methods in Fluids, Vol. 56, pp. 877-898 (SCI) [6] P. H. Chiu, Tony W. H. Sheu, R. K. Lin (2008), An effective explicit pressure gradient scheme implemented in the twolevel non-staggered grids for incompressible Navier-Stokes equations, Journal of Computational Physics, Vol. 227, pp. 4018-4037 (SCI) [7] Tony W. H. Sheu, H. P. Rani, T. C. Tan, S. F. Tsai (2008), Multiple states, topology and bifurcations of natural convection in a cubical cavity, Computers and Fluids, Vol. 37, pp. 1011-1028 (SCI) [8] Tony W. H. Sheu, C. F. Chen, L. W. Hsieh (2008), Development of a three-point sixth-order compact Helmholtz scheme for scattering wave propagation, Journal of Computational Acoustics (accepted) (SCI)

[9] V. C. Huang, Tony W. H. Sheu (2008), Tissue fluids in microchannel subjected to an externally applied electric potential, International Journal of Numerical Method for Heat and Fluid Flow (accepted) (SCI) [10] Harry Y. H. Chen, Tony W. H. Sheu (2008), Development of a monotonic upwind convection-diffusion finite element model in two dimensions, International Journal for Numerical Methods in Fluids (in press) (SCI) [11] V. C. Huang, Tony W. H. Sheu (2008), Heat transfer involved in acupuncture with burning moxibustion on the top of the handel of the acupuncture needle, Acupuncture & Electro-Therapeutics Research (accepted)

[12] Y. F. Chau, D. P. Tsai, L. F. Shen, T. J. Yang, Y. S. Sun, "The Plasmon and distribution effects between incident light and active layer in PtO x -type superresolution near-field structure, "Optics Communication 281, 1293-1299 (2008). [13] K.P. Chiu, T.S. Kao, D.P. Tsai, "Evanescent field enhancement due to plasmonic resonances of a metamaterial slab, " Journal of Microscopy 269, 313319 (2008). [14] T. S. Kao, Y. H. Fu, H. W. Hsu, D. P. Tsai, "Study of the optical response of phasechange recording layer with zinc oxide nanostructured thin film, " Journal of Microscopy 229, 561

D.11 Regional Programs in Hsinchu D.11.1 Matrix Computation Coordinator: Wen-Wei Lin (National Tsing Hua University/National Chiao Tung University)

n view of the potential of the realworld applications, without doubt, Scientific Computation (SC) becomes a rapidly growing multidisciplinary research area. Based on the support of NCTS in the past years, the SC group gets blooming. The SC program at NCTS has been getting cooperation with the PDE, Mathematical Biology, and Dynamical Systems programs in Mathematics Division. In this academic year (2007/9~2008/8), SC group at NCTS particularly strengthened the frontier topic on the structured eigenvalue problems which usually arise from the applications of vibration analysis of highspeed train, surface acoustic wave filter, and molecular biology etc. We now report the activities of SC group in this year. We have organized one international workshop and a one-semester graduate course. Meanwhile, we also have invited a number of distinguished

researchers to offer some short courses and to conduct cooperative research with our community. A summary of our activities lists below.

I. International Workshop Recent Advances in Numerical Methods for Eigenvalue Problems (RANMEP2008), January 4-8, 2008 The purpose of the workshop is to provide a forum for numerical analysts, application scientists and engineers to present the latest progress on numerical methods for solving eigenvalue problems and discuss some of the challenges they are facing. Topics of the workshop include (i) methods for solving large-scale eigenvalue problems, (ii) structurepreserving methods for the structured eigenvalue problems, (iii) eigenvalue applications in control, quantum physics and


chemistry, and accelerator design etc. The workshop brings some of the world's leading experts in these fields together and aims at (1) providing an opportunity for direct communication and exchange of ideas; (2) promoting interaction and collaboration of local and international scholars. The workshop included 14 foreign invited speakers, Peter Arbenz (ETH Zurich, Switzerland), Peter Benner (Chemnitz University of Technology, Gremany), Zhaojun Bai (University of California, USA), Francois Gygi (University of California Davis, USA), Do-Young Kwak (Korea Advanced Institute of Science and Technology, Korea), Fong Yin Lim (National University of Singapore, Singapore), Volker Mehrmann (Technische Universitat Berlin, Gremany), Axel Ruhe (Royal Institue of Technology, Sweden), Tetsuya Sakurai (University of Tsukuba, Japan), Danny Sorensen (Rice University, USA), Yangfeng Su (Fudan University, China), Heinrich Voss (Hamburg University of technology, Gremany), Qiang Ye (University of Kentucky, Canada), Zhonggang Zeng (Northeastern Illinois University, USA), and total number of participant is 100 roughly.

II. Autumn Graduate Course NCTS & NTHU Topical Program in Structured Matrix Computation, September - December 2007

The purpose of the course is to introduce real application problems and the potential numerical methods to the researchers and graduate students who are working on SC. The problems and numerical methods include especially, polynomial eigenvalue problems, palindromic quadratic eigenvalue problems, Maxwell equation in numerical computations and structure-preserving algorithms for vibration of fast trains or electrics problems, etc. Seven lecturers, Wen-Wei Lin (NTHU), Tsung-Min Hwang (NTNU), Wei-Cheng Wang (NTHU), Chin-Tien Wu (NCTU), Yin-Liang Huang (NTHU), Chern Shuh Wang (NCKU), Weichung Wang (NTU), share the course which consists of several different topics related to eigenvalue problems and numerical methods.


1. Jacobi-Davidson Method for Large Sparse Eigenvalue Problems, 2. Structure-Preserving Doubling Algorithms, 3. Structure Algorithms for Palindromic Quadratic Eigenvalue Problems: Vibration of Fast Trains, 4. Jacobi-Davidson Method for Polynomial Eigenvalue Problems, 5. Numerical Simulation of Jacobi-Davidson Methods, 6. Projection-Free Jacobi-Davidson Methods for Maxwell Equation, 7. Finite Element Modelling of Fast Train Rails, Palindromic Eigenvalue Problem, 8. Numerical Computation of Maxwell Equations, 9. Fast Fourier Transformation.

III. Short Term Visitors 1. Professor Alastair Spence (University of Bath, United Kingdom) Nov. 27 - Nov. 30, 2007 2. Professor Ren-Cang Li (University of Texas at Arlington, USA) Jun. 5 - Jul. 4, 2008 Prof. Li visited NCTS one month in this summer and presented three talks: 1. Structure-Preserving Model Reduction. 2. Analysis for Nonlinear Dimensionality Reduction Algorithms. 3. Vandermonde Matrices with Applications to Convergence Analysis of CG and Lanczos Algorithms. In addition, he finished one paper with Wen-Wei Lin and Chern-Shuh Wang.

3. Professor Yuen-Cheng Kuo (National University of Kaohsiung) Jun. 19 - Sep. 18, 2008 Prof. Kuo visited NCTS two months in this summer and focused on "palindromic eigenvalue problem" to develop a more effective transformation rather than S+S -1transformation. In addition, he also completed

a joint work related to nonlinear Schrodinger equations.

our group. In the mean time, he completed two joint works.

1. "A Hyperplane-Constrained Continuation Method for Bound States of Coupled Nonlinear Schrodinger Equations", Yuen-Cheng Kuo, Wen-Wei Lin, Shih-Feng Shieh and Weichung Wang.

1. "On the *-Sylvester Equation AX ± X*B*= C", Chun-Yueh Chiang, Eric King-Wah Chu and Wen-Wei Lin.

4. Professor Tsung-Min Hwang (National Taiwan Normal University) Jun. 20 - Sep. 19, 2008 Prof. Hwang visited NCTS about two months in this summer and finished three joint papers with the fellows of SC group. 1. "Structured Algorithms for Palindromic Quadratic Eigenvalue Problems Arising in Vibration of Fast Trains", Tsung-Min Hwang, Wen-Wei Lin and Jiang Qian. 2. "Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case", ChunYueh Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-Wei Lin and Shu-Fang Xu. 3. "Structured doubling algorithms for solving g-palindromic quadratic eigenvalue problems", Eric King-wah Chu, Tsung-Ming Huang and Wen-Wei Lin.

5. Professor Chern Shuh Wang (NCKU) Jul. 1 - Sep. 15, 2008 Prof. Wang introduced some his recent results on the structure-preserving algorithm and then he finished a joint work with RenCang Li and Wen-Wei Lin. 1. "Structured Backward Error for Palindromic Polynomial Eigenvalue Problems", Ren-Cang Li, Wen-Wei Lin and Chern-Shuh Wang.

6. Professor Eric Chu (Monash University, Australia) Jul. 3 - Aug. 2, 2008 Prof. Chu visited NCTS one month this year and continued doing further work with

2. "Convergence Analysis of the Doubling Algorithm for Several Nonlinear Matrix Equations in the Critical Case", ChunYueh Chiang, Eric King-Wah Chu, Chun-Hua Guo, Tsung-Ming Huang, Wen-Wei Lin and Shu-Fang Xu

7. Professor Ting-Hui Yang (Tamkang University) Jul. 15 - Sep. 15, 2008 Prof. Yang visited NCTS two months this summer and finished two papers as follows. 1. "Viscous standing asymptotic states of transonic flows through a nozzle of varying area", John M. Hong, Ting-Hui Yang and Weishi Liu. 2. "Diversity of traveling waves in FitzHugh-Nagumo type equations", Cheng-Hsiung Hsu, Ting-Hui Yang and Chi-Ru Yang.

8. Professor Edward Allen (Texas Tech. University) Aug. 1 - Aug. 14, 2008 Although Prof. Allen visited NCTS only two weeks, he provided us a short course entitled "Modeling Techniques and Numerical Methods for Stochastic Differential Equations" which introduce some state of the art modeling techniques in the world. After his series talks, he also gave us a 350-page lecture note.

9. Professor Chun-Hua Guo (University of Regina, Canada) Mar. 1 - Jun. 30, 2009 Prof. Guo plans to visit NCTS in next spring. However, he is already an active collaborator with our group. Recently he cooperated with Wen-Wei Lin to finish a paper as follows. "Convergence Rate of the Cyclic Reduction Algorithm for Null Recurrent Quasi-Birth-Death Problems", Chun-Hua Guo and Wen-Wei. Lin.


D.11 Regional Programs in Hsinchu D.11.2 Nonlinear Partial Differential Equations Coordinators: Chern Jann-Long (National Central University, CTS) Tai-Chia Lin (National Taiwan University)

I. Activity of Visiting Scholars

Title: TBA (3) Junping Shi, College of Willian and Mary, USA

s follows are the contents of lectures and activities of our visiting scholars. • Emilio Acerbi (University of Parma, Italy) 2007/09/20-2007/10/03: Calculus of Variations, Parabolic PDE • J. Bao (North Carolina UNCC) 2007/12/22007/12/23: PDE • Jann-Long Chern (National Central University) 2007/08-2008/07: Elliptic PDE • G. El (Loughborough University, United Kingdom) 2008/03/19-2008/04/01: Nonlinear waves, Solitons, Fluid dynamics

Title: Standing Pulse solution of a reactiondiffusion equation of logistic growth (4) Tai-Chia Lin, Taiwan University, Taiwan Title: Orbital stability of bound states of semi-classical nonlinear Schrodinger equations with critical nonlinearity (5) Jann-Long Chern, Central University, Taiwan Title: Uniqueness of Topological Solutions and the Structure of Solutions for the Chern-Simons Equations with Two Higgs Particles

Other visitors include: Chi-Hun Lin (National Chiao Tung University), Y. Morita (Ryukoku University), Juncheng Wei (The Chinese University of HongKong), LieJune Shiau (University of Houston), Tien-Tsan Shieh (University of Arizona)

Taiwan-Tohoku Seminar on Differential Equations, April 15, 2008

II. Conferences

Place: Tohoku University, Godo-To 802

Partial Differential Equations Day, November 28 (Wednesday), 2007

Invite Speakers:

Organizer: Jann-Long Chern (National Central University, NCTS) Tai-Chia Lin (National Taiwan University) Invite Speakers: (1) Eiji Yanagida, Tohoku University, Japan Title: Singular solutions of the Fujita-type equation (2) Kunimochi Sakamato, University, Japan


Hiroshima

Organizer: Jann-Long Chern (National Central University, NCTS, Taiwan) Eiji Yanagida (Tohoku University, Japan)

(1) Shota Sato (Tohoku University) Title: Solutions with Moving Singularties for a Semilinear Parabolic Equation (2) Zhi-You Chen University)

(National

Central

Title: the Classification of Standing Wave Solutions for the Schrodinger Equation (3) Masaki Hoshino (Tohoku University) Title: Rate of Approach of Two Solutions for a Semilinear Parabolic Equation with Power Nonlinearity

(4) Yong-Li Tang University)

(National

Central

Title: The Structure of Tadial Solutions for Elliptic Equations Arising from the spherical Onsager Vortex (5) Tatsuki Kawakami (Tohoku University)

Instructor: Junging Shi ( ) (Department of Mathematics, College of William and Mary, Virginia, USA) Time: F2, F3, F4 ( 96 Place:

III. Courses NTHU & CMS & NCTS Joint Course on Bifurcation theory in Banach space and application to semilinear elliptic equations and systems

: MATH 610100

NCTS& NTHU Joint Course on Nonlinear Analysis and Semilinear Elliptic Problems , 2008/02-2008/06 Instructor: Jann-Long Chern (

)

Time: F2, F3, F4 ( 97

, 2007/09-2008/01

9:00 - 12:00), 14

Room 631

(6) Jann-Long Chern (National Central University) Title: On the Uniqueness and Structures of Solutions for the Self-Dual Chern-Simons Model

9

Place:

2

9:00 - 12:00), 22

Room 734, : MATH 657400

D.12 Regional Programs in Taipei D.12.1 Algebraic Geometry--Three dimensional birational geometry Coordinator: Jung-Kai Chen (National Taiwan University)

I. Research achievements

inimal model program is one of the main stream in the research of algebraic geometry. Even though there is a satisfactory theory in dimension three, there are still many interesting and important problems remaining. In this past year, Meng Chen and Jungkai Chen developed a systematical way of studying three-dimensional singularities. It was first introduced to solve the problem on pluricanonical maps of general type. In the past year, we developed the theory of baskets

furthermore. Its geometric realization, and some more applications was discovered. More precisely, the behavior of baskets under elementary birational maps is studied. It turns out that one can prove an effective termination of flips in dimension three as an application. Moreover, one can obtained an application in classification of weak Q-Fano threefold, where the sharp lower bound for anti-canonical volume is proven to be 1/330. These works solved many open problems in the birational geometry of threefolds. One can also expect these works have some more applications, especially in some effectiveness or finiteness problems in dimension three.


Professor Kollár (Princeton University) had invited us to present an announcement, which was published in the prestigious journal Elec. Res. Announc. Math. Sci., 14, 69-73, (2007).

II. Publications related to this topic in recent years

0704.1702 J. A. Chen, M. Chen, An optimal boundedness on weak $\bQ$-Fano threefolds, Adv. Math., to appear. arXiv 0712.4356 J. A. Chen, M. Chen, Explicit birational geometry of threefolds of general type, submitted. arXiv 0706.2987

F. Campana, J. A. Chen, T. Peternell, On strictly nef divisors, Math. Ann., to appear. arXiv 0511042

J. A. Chen, C. D. Hacon, On Ueno's Conjecture K, submitted. arXiv 0802.1060.

J.A. Chen, M. Chen, The canonical volume of threefolds of general type with X K pi, phi K and rho K in NLO PQCD", Wei-Shu Hou , Hsiang-nan Li , Satoshi Mishima , Makiko Nagashima , Phys.Rev.Lett.98:131801, 2007. [2] "Okubo-Zweig-Iizuka-rule violation and B ---> eta-(prime) K branching ratios", JenFeng Hsu, Yeo-Yie Charng, Hsiang-nan Li, Phys.Rev.D78:014020, 2008

[3] "Next-to-leading-order corrections to exclusive processes in k(T) factorization", Soumitra Nandi, Hsiang-nan Li. Phys.Rev.D76:034008, 2007. [4] "Factorization approaches to B meson decays", Hsiang-nan Li. FPCP-2007-011, In the Proceedings of 5th Flavor Physics and CP Violation Conference (FPCP 2007), Bled, Slovenia, 12-16 May 2007. arXiv:0707.1294 [hep-ph] [5] "Possible complex annihilation and B ---> K pi direct CP asymmetry", Junegone Chay, Hsiang-nan Li , Satoshi Mishima, MIT-CTP-3902. arXiv:0711.2953 [hepph], accepted for publication in Phys. Rev. D. [6] "Comment on 'Gauge Invariance and $k_T$-Factorization of Exclusive Processes", Hsiang-nan Li . arXiv: 0808.1526 [hep-ph] [7] "Constraints on Unparticle Interaction from b ---> s gamma", Xiao-Gang He, Luhsing Tsai, JHEP 0806:074, 2008. [8] "Rare Decays with a Light CP-Odd Higgs Boson in the NMSSM", Xiao-Gang He, Jusak Tandean, G. Valencia, JHEP 0806:002, 2008. [9] "Unparticle Induced Baryon Number Violating Nucleon Decays", Xiao-Gang He, Sandip Pakvasa. Phys.Lett.B662:259263, 2008. [10] "Supersymmetric Unparticle Effects on Higgs Boson Mass and Dark Matter", N.G. Deshpande, Xiao-Gang He, Jing Jiang, Phys.Lett.B656:91-95, 2007. [11] "Constraints on unparticle interactions from invisible decays of Z, quarkonia and neutrinos", Shao-Long Chen, Xiao-Gang He, Ho-Chin Tsai, JHEP 0711:010, 2007. [12] "SUSY R-parity violating contributions to the width differences for D - anti-D and B(d,s) - anti-B(d,s) systems", ShaoLong Chen, Xiao-Gang He, A. Hovhannisyan, Ho-Chin Tsai , JHEP 0709:044,2007. [13] "Interactions of Unparticles with Standard Model Particles", Shao-Long Chen, Xiao-Gang He, Phys.Rev.D76: 091702, 2007

119 ‹‹- Highlights of Programs

[14] "Spontaneous CP violating phase as the CKM matrix phase", Shao-Long Chen, N.G. Deshpande, Xiao-Gang He, Jing Jiang, Lu-Hsing Tsai, Eur.Phys.J.C53: 607-614,2008. [15] "D - anti-D mixing constraints on FCNC with a non-universal Z-prime", XiaoGang He, German Valencia, Phys.Lett. B651:135-138, 2007. [16] "Scalar dark matter effects in Higgs and top quark decays", Xiao-Gang He, Tong Li, Xue-Qian Li, Ho-Chin Tsai, Mod.Phys.Lett.A22:2121-2129, 2007 [17] "A(4) group and tri-bimaximal neutrino mixing: A Renormalizable model", XiaoGang He, Nucl.Phys.Proc.Suppl.168:350352, 2007. [18] "Does the HyperCP Evidence for the Decay Sigma --> p mu+ mu- Indicate a Light Pseudoscalar Higgs Boson", XiaoGang He, Jusak Tandean, G. Valencia, Phys.Rev.Lett.98:081802, 2007 [19] "Calculation of BR(anti-B0 ---> Lambda(c)+ + anti-p) in the PQCD approach", Xiao-Gang He, Tong Li, XueQian Li, Yu-Ming Wang, Phys.Rev. D75:034011,2007. [20] "Minimal modification to the tribimaximal neutrino mixing", Xiao-Gang He, A. Zee. Phys.Lett.B645:427-431, 2007. [21] "Shear Viscosity of a Non-Relativistic Conformal Gas in Two Dimensions", Jiunn-Wei Chen, Wen-Yu Wen, arXiv:0808.0399 [hep-th]. [22] "Bulk viscosity of a gas of massless

Highlights of Programs -›› 120

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30]

pions", Jiunn-Wei Chen , Juven Wang, arXiv:0711.4824 [hep-ph]. "Phase Transitions and the Perfectness of Fluids", Jiunn-Wei Chen, Mei Huang, Yen-Han Li, Eiji Nakano, Di-Lun Yang, arXiv:0709.3434 [hep-ph]. "Universality of mixed action extrapolation formulae". Jiunn-Wei Chen, Donal O'Connell, Andre "Walker-Loud, arXiv:0706.0035 [hep-lat]. "QCD viscosity to entropy density ratio in the hadronic phase", Jiunn-Wei Chen, Yen-Han Li, Yen-Fu Liu, Eiji Nakano, Phys.Rev.D76:114011, 2007. "Generalised parton distributions of the pion in partially-quenched chiral perturbation theory", Jiunn-Wei Chen, William Detmold, Brian Smigielski, Phys.Rev.D75:074003, 2007. "BEC-BCS Crossover in the Epsilon Expansion", Jiunn-Wei Chen, Eiji Nakano, Phys.Rev.A75:043620, 2007. "Shear viscosity to entropy density ratio of QCD below the deconfinement temperature", Jiunn-Wei Chen, Eiji Nakano, Phys.Lett.B647:371-375, 2007. "Self-Adjoint Extensions of the Hamiltonian Operator with Symmetric Potentials which are Unbounded from Below", H.-T. Cho and C.-L. Ho, J. Phys. A 41,255308, 2008. "A Novel Quasi-Exactly Solvable Model with Total Transmission Modes", H.-T. Cho and C.-L. Ho, J. Phys. A 41, 172002, 2008.

Focus Group on Strings Coordinator: Hsien-chung Kao (National Taiwan Normal University, email:[email protected]) Committee members: Chuan-Tsung Chan (TungHai University), Chiang-Mei Chen (National Central University), Kazuyuki Furuuchi (National Center for Theoretical Sciences), Choon-Lin Ho (Tamkang University), Pei-Ming Ho (National Taiwan University), Jen-Chi Lee (National Chiao Tung University), Feng-Li Lin (National Taiwan Normal University).

I. Brief Description

here are eleven postdocs members: Pravina Borhade (TungHai University), Takayuki Hirayama (NCTS), Peter Matlock (Nat'l Chiao Tung University), Toshihiro Matsuo (Nat'l Taiwan Normal University), Makoto Narita (Nat'l Taiwan University), Dmitry Orlov (Nat'l Central University), Tomohisa Takimi (NCTS & Nat'l Chiao Tung University), Dan Tomino (Nat'l Taiwan Normal University), Wen-Yu Wen (Nat'l Taiwan University), Yi Yang (NCTS & Nat'l Chiao Tung University) and Syoji Zeze(Nat'l Taiwan University). There are also about six student members. The main purpose for this focus group is to enhance the interaction and collaboration among the group members. It is fair to say that so far the string focus group does live up to our expectation and most of our members are satisfied with the way it is run, thanks to the effort of the previous coordinators, Pei-Ming Ho and JenChi Lee. Currently, we have regular seminars at NTU, NTHU and NTNU. If some members are interested in certain specific topics, we would also ask our visitors to give review lectures on these topics. Through these activities, we have established a close connection with the Japanese string community. Last year, we had more than twenty visitors from Japan. In addition, many of our group members were invited to go to Japan to talk about their works. A lot of collaborations have been generated through these visits. In August, Chuan-Tsung Chan organized a two-day mini-workshop on little

strings. There were about twenty participants. In the past few years, research topics investigated by the group members include AdS/CFT string duality and its applications, non-commutative geometry, string cosmology, string high energy scattering, string black holes, quasi-normal modes in black holes and quasi exactly solvable models.

II. Activities 1. Weekly string seminars at NTU The schedule is announced at http://web.phys.ntu.edu.tw/string/index.htm. The record of past seminars can be found at http://phys.cts.ntu.edu.tw/fgroup.aspx?mclass= 4&fclass=2&aclass=7. This is the core activities of the group. This series of seminars was initiated in 1996. It is scheduled in the Friday afternoon so that most group members can attend. The talks are given either by group members or by invited visitors from oversea to present their recent works. It usually lasts for two hours so that details of the work can be explained to some extent and participants have enough time to ask questions. After the seminar, members would usually stay for further discussion with the speaker or with one another. It is important for generating collaborations and bonding the group members. 2. Biweekly high energy seminar at NTNU The schedule is announced at http://home.phy.ntnu.edu.tw/~highenergy/. This series of seminars includes topics such as cosmology and particle physics so that the group members have a chance to interact with physicists from other fields. Many foreign visitors visiting NTU also spend a few days in


NTNU for giving additional talks or having further discussion. 3. Biweekly high energy seminar at NTHU There are now five faculty and postdocs members in the Hsinchu area and regular seminars have been arranged since last year. Kazuyuki Furuuch has been very active in inviting visitors who would usually stay in NCTS for a few days. He has also asked several of our visitors to give review lectures in NCTS if some members are interested in certain specific topics. 4. Mini-Workshop on Matrix and String Chuan-Tsong Chan organized a two-day mini-workshop on August 4 and 5. It is announced at http://phys.cts.ntu.edu.tw/data/ 97.8.4poster.pdf. There are two series of lectures: Minimal String Theory and IKKT Model given by three speaker, David Shih (IAS), Hirotaka Irie (NTU) and Dan Tomino (NCTS). There were about twenty participants.

III. Visitors and International Collaborations The string focus group has maintained a steady and close connection with the Japanese string community thanks to the effort of Prof. Takeo Inami of Chou University. In the past few years, we have about thirty oversea visitors each year. A summary of the information about these visits in last year can be found at http://phys.cts.ntu.edu.tw/ fgroup.aspx?mclass=3&dclass=1&fclass=2. About two thirds of them are from Japan. Many of them even pay for their own airfare and we only need to pay for their local expanses. That is the reason why we can afford to invite many Japanese string theorists to visit us. In addition, many of our group members have been invited to go to Japan to talk about their works. A lot of collaborations have been generated through these visits. In the future, we would like to strengthen our connection to the string communities in other Asian countries, such as South Korea, India and Mainland China. Below is a summary of the group members' visits of oversea institutions in the past year.


1. Choon-Lin Ho is visiting YITP, hosted by Prof. Ryu Sasaki, form 6/12 to 9/11 and will visit Tokyo University, hosted by Prof. Yutaka Matsuo, in September. 2. Kazuyuki Furuuch visited YITP for a KIAS-YITP joint workshop on String Phenomenology and Cosmology from September 24 to 28 and Riken for the Riken Symposium "String Field Theory 07" from October 6 to 7 in 2007. He also visited KEK from October 9 to 12 in 2007. He was hosted by Prof. Yoshihisa Kitazawa and gave a talk titled "Matrix model for Polyakov loops, string field theory in the temporal gauge, and winding string condensation in Anti-de Sitter space" there. 3. Jen-Chi Lee visited Tokyo University, hosted by Prof. Yoneya, from April 9 to July 8 in 2007. He is visiting YITP, hosted by Prof. Sasaki, from July 15 to August 15, 2008. 4. Feng-Li Lin attended Strings 2007 in Mardid. He also went to a String cosmology workshop at YITP in September of 2007.

IV. Highlights of Research Results 1. Lie 3-Algebra and Multiple M2-branes In the past few months there has been a surge in interest in the Lie three-algebra, which lays down the mathematical foundation for understanding multiple M2 and M5 branes. Pei-Ming Ho and his student Ru-Chuen Hou, collaborating with Japanese string theorists, have made important contribution on this topic. Two of their papers (number 2 and 4) have been cited more than fifty times according to the statistics by Spires. References [1] Pei-Ming Ho, Yosuke Imamura, Yutaka Matsuo and Shotaro Shiba, "M5-brane in three-form flux and multiple M2-branes", arXiv: 0805.2898, JHEP 0808:014, 2008. [2] Pei-Ming Ho, Yosuke Imamura and Yutaka Matsuo, "M2 to D2 revisited", arXiv: 0805.1202, JHEP 0807:003, 2008. [3] Pei-Ming Ho and Yutaka Matsuo, "M5

from M2", arXiv: 0804.3629, JHEP 0806:105, 2008. [4] Pei-Ming Ho, Ru-Chuen Hou and Yutaka Matsuo, "Lie 3-Algebra and Multiple M2branes", arXiv: 0804.2110, JHEP 0806:020, 2008. 2. High Energy String Scatterings This is a long term project started in 2003. It is based on many earlier works of Jen-Chi Lee in 90's. Following a breakthrough of Chuan-Tsung Chan and Jen-Chi Lee in 2003, The Taiwan string group has published more than 15 papers on this single subject and about half of the group members participated in the project. Although these works are not well recognized, they are truly initiated in Taiwan. Hopefully they will attract more attention in the near future. In 2006, Chuan-Tsung Chan, Jen-Chi Lee and Yi Yang generalized the linear relations (stringy symmetry) to include Dbranes. More importantly, Jen-Chi Lee and Yi Yang have shown the coexistence of the linear relations and the softer exponential fall-off behavior of high energy string scattering amplitudes. They have also discovered some interesting string scatterings which has an unusual power-law behavior at high energy. More recently, Jen-Chi Lee and Yi Yang, together with Prof. Yoneya of Tokyo University, are trying to fit their results to Yoneya's "space time uncertainty relation". References [1] Jen-Chi Lee, Yi Yang, "High-energy Massive String Scatterings from Orientifold Planes", 0712.4245, Nucl.Phys.B798:198-209, 2008. [2] Jen-Chi Lee and Yi Yang,"Power-law Behavior of High Energy String Scatterings in Compact Spaces", 0709.4657, Phys.Conf.Ser.110:102007, 2008. [3] Jen-Chi Lee and Yi Yang, "Linear Relations and their Breakdown in High Energy Massive String Scatterings in Compact Spaces", 0705.1872, Nucl.Phys.B784, 22 (2007). [4] Jen-Chi Lee and Yi Yang,"Linear relations of high energy absorption/emission

amplitudes of D-brane", hep-th/0612059, Phys.Lett.B646, 120 (2007). [5] Jen-Chi Lee,"Zero-norm states and superstringy symmetries", hep-th/0610272 (to be published by World Scientific). [6] Chuan-Tsung Chan, Jen-Chi Lee and Yi Yang,"Power-law behavior of strings scattered from domain-wall at high energies and breakdown of their linear relations", hep-th/0610219. [7] Chuan-Tsung Chan, Jen-Chi Lee and Yi Yang, "Scatterings of massive string states from D-brane and their linear relations at high energies",hep-th/0610062, Nucl. Phys.B764, 1 (2007). [8] Chuan-Tsung Chan, Jen-Chi Lee and Yi Yang, "Notes on High energy limit of Bosonic closed string scattering amplitudes", hep-th/0604122, Nucl.Phys.B749, 280 (2006). [9] Pei-Ming Ho and Xue-Yan Lin, "Linear relations among 4-point functions in the high energy limit of string theory", Phys.Rev.D73, 126007 (2006). 3. AdS/CFT Duality and Its Applications AdS/CFT and its possible application to QCD remains one of the focus in the string community. By studying the gravity dual of supersymmetric Yang-Mills theories, it is hoped that certain non-perturbative aspect of QCD can be understood. Many group members have published works on this topic. References [1] Chong-Sun Chu and Pei-Ming Ho, "Timedependent AdS/CFT duality. II. Holographic reconstruction of bulk metric and possible resolution of singularity", arXiv: 0710.2640, JHEP 0802:058, 2008. [2] Feng-Li Lin, Toshihiro Matsuo and Dan Tomino, "Hagedorn Strings and Correspondence Principle in AdS(3)", arXiv:0705.4514, JHEP 0709:042, 2007. [3] Koji Hashimoto , Takayuki Hirayama, Feng-Li Lin and Ho-Ung Yee, "Quark Mass Deformation of Holographic Massless QCD", arXiv: 0803.4192, JHEP 0807:089, 2008.


[4] Eiji Nakano and Wen-Yu Wen, "Critical magnetic field in a holographic superconductor", arXiv: 0804.3180, Phys.Rev.D78:046004, 2008. [5] Wen-Yu Wen, "2D Heisenberg model from rotating membrane", arXiv: 0705.263 Nucl.Phys.B791:164-174, 2008. [6] Eiji Nakano, Shunsuke Teraguchi and Wen-Yu Wen, "Drag force, jet quenching, and AdS/QCD", hep-ph/0608274, Phys.Rev.D75: 085016, 2007. [7] Wen-Yu Wen, "Spin chain from marginally deformed AdS(3) x S**3," hepth/0610147, Phys.Rev.D75: 067901, 2007. 4. Gravity and Cosmology Gravity and cosmology are close related to string theories. In particular, understanding black holes is important for making progress in quantum gravity. References [1] R0ong-Gen Cai, Chiang-Mei Chen , Keiichi Maeda, Nobuyoshi Ohta and Da-Wei Pang, "Entropy Function and Universality of Entropy-Area Relation for Small Black Holes", arXiv:0712.4212, Phys.Rev.D77: 064030, 2008. [2] Adel Bouchareb, Gerard Clement, ChiangMei Chen, Dmitri V. Gal'tsov, Nikolai G. Scherbluk and Thomas Wolf, "G(2) generating technique for minimal D=5 supergravity and black rings", arXiv:0708.2361, Phys. Rev. D76:104032, 2007. [3] Chiang-Mei Chen, Dmitri V. Gal'tsov and Dmitry G. Orlov, "Extremal black holes in D=4 Gauss-Bonnet gravity", hepth/0701004, Phys.Rev.D75: 084030, 2007. [4] S.A. Kononogov and D.G. Orlov, "Variation of the gravitational constant in S-brane cosmology, "Grav.Cosmol.13:185190, 2007. [5] Hsien-chung Kao and Dan Tomino, "Quasinormal Modes of Kerr Black Holes in Four and Higher Dimensions", arXiv: 0801.4195, Phys.Rev.D77:127503, 2008. [6] Hsien-chung Kao, "Second Order Perturbative Calculation of Quasinormal


Modes of Schwarzschild Black Holes", arXiv: 0704.0284, Phys.Rev.D75:124008, 2007. 5. International Collaborated Papers References [1] V.R. Khalilov and Choon-Lin Ho, "Scattering of spin-polarized electron in an Aharonov-Bohm potential," arXiv: 0708.3131, Annals Phys.323:1280-1293, 2008. [2] Choon-Lin Ho and Ryu Sasaki, "Deformed multi-variable Fokker-Planck equations," cond-mat/0703291, J. Math. Phys. 48:073302, 2007. [3] N.D. Hari Dass and Peter Matlock, "Covariant Calculus for Effective String Theories," arXiv:0709.1765. [4] Tsunehide Kuroki and Toshihiro Matsuo, "Production cross section of rotating string," arXiv:0712.4062, Nucl.Phys. B798:291-309, 2008. [5] Pei-Ming Ho, Yosuke Imamura, Yutaka Matsuo and Shotaro Shiba, "M5-brane in three-form flux and multiple M2-branes", arXiv: 0805.2898, JHEP 0808:014, 2008. [6] Pei-Ming Ho, Yosuke Imamura and Yutaka Matsuo, "M2 to D2 revisited", arXiv: 0805.1202, JHEP 0807:003, 2008. [7] Pei-Ming Ho and Yutaka Matsuo, "M5 from M2", arXiv: 0804.3629, JHEP 0806:105, 2008. [8] Pei-Ming Ho, Ru-Chuen Hou and Yutaka Matsuo, "Lie 3-Algebra and Multiple M2branes", arXiv: 0804.2110, JHEP 0806:020, 2008. [9] Chong-Sun Chu and Pei-Ming Ho, "Timedependent AdS/CFT duality. II. Holographic reconstruction of bulk metric and possible resolution of singularity", arXiv: 0710.2640, JHEP 0802:058, 2008. [10] Koji Hashimoto , Takayuki Hirayama, Feng-Li Lin and Ho-Ung Yee, "Quark Mass Deformation of Holographic Massless QCD", arXiv: 0803.4192, JHEP 0807:089, 2008. [11] Rong-Gen Cai, Chiang-Mei Chen , Keiichi Maeda, Nobuyoshi Ohta and Da-Wei

Pang, "Entropy Function and Universality of Entropy-Area Relation for Small Black Holes", arXiv: 0712.4212, Phys.Rev.D77: 064030, 2008. [12] Adel Bouchareb, Gerard Clement, Chiang-Mei Chen , Dmitri V. Gal'tsov, Nikolai G. Scherbluk and Thomas Wolf , "G(2) generating technique for minimal D=5 supergravity and black rings", arXiv:0708.2361, Phys. Rev. D76: 104032, 2007. [13] Chiang-Mei Chen, Dmitri V. Gal'tsov and Dmitry G. Orlov, "Extremal black holes in D=4 Gauss-Bonnet gravity", hepth/0701004, Phys.Rev.D75: 084030, 2007. [14] S.A. Kononogov and D.G. Orlov, "Variation of the gravitational constant in S-brane cosmology, "Grav.Cosmol. 13:185-190, 2007. 6. Talks Presented in International Conferences References [1] Choon-Lin Ho, "Prepotential approach to exact and quasi-exact solvabilities of

Hermitian and non-Hermitian Hamiltonians," Talk given at Conference in Honor of C.N. Yang's 85th Birthday: Statistical Physics, High Energy, Condensed Matter and Mathematical Physics, Singapore, 31 Oct - 3 Nov 2007. arXiv:0801.0944. [2] Kazuyuki Furuuchi, "Matrix Model For Polyakov Loops, String Field Theory In The Temporal Gauge, Winding String Condensation In Anti-de Sitter Space And Field Theory Of D-branes," Talk given at International Symposium on Cosmology and Particle Astrophysics (COSPA 2007), Taipei, Taiwan, 13-15 Nov 2007. arXiv:0806.4800. [3] Chiang-Mei Chen, "Extremal dilatonic black holes in 4D Gauss-Bonnet gravity," 8th Asia - Pacific International Conference on Gravitation and Astrophysics (ICGA8): For the 100th Anniversary of Hideki Yukawa and Protomotion of Women Scientists (ICGA8), Nara, Japan, 29 Aug 1 Sep 2007. Prog.Theor.Phys.Suppl. 172:161-164, 2008. arXiv:0801.0032.


Highlights of Programs Interdisciplinary Fields Focus Group on Atomic, Molecular and Optical Physics Coordinator: Daw-Wei Wang (National Tsing Hua University; email: [email protected]) Committee members: Ying-Cheng Chen (IAMS),Chung-Hou Cheng (National Chiao Tung University), |Shin-Chuan Gou (National Changhua University of Education), Dian-Jiun Han (National Chung Cheng University), Tsin-Fu Jiang (NCTU), Jiang-Nan Liu (Fu-Jen Catholic University), Yi-Wei Liu (National Tsing Hua University), Wen-Chin Wu (National Taiwan Normal University)


roup size: Active faculty members are about 20, including experimentalists. Goal: 1) To encourage more cooperation between faculty in this community, including cooperation between theorists and experimentalist. 2) To attract more researchers/ students to join to form a stable research environment. 3) To enhance the research quality by actively cooperating with international frontier researchers and concentrating on some promising projects. Research direction: Our FG encourages the following four directions of research: (1) Strongly correlated effects in cold atoms: It is well-known that cold atom systems are a very excited systems for studying quantum many-body system in a much controllable methods than any other


systems before. By combining analytic and numerical methods developed recently, we hope to explore the exotic many-body phases of cold atom systems as well as the dynamical and finite temperature properties, which can be important to its future application of quantum physics. (2) Weakly interacting Bose gases: A certain portion of our group members have developed their own numerical technique to study the static as well as the dynamic properties of Bose-Einstein condensation of cold atoms in the mean-field level and beyond. Several analytic works on the transition temperature properties of interacting bosonic atoms as well as magnetic dipoles are developed. (3) Atomic structure theory: We have had a good start in atomic structure theory in the past few years when Prof. Tu-Nan Chang (USC, USA) was in Taiwan as NCTS director. We will keep such cooperation ongoing and encourage more national-wide activities in this subfield. (4) Intensive laser and plasma: Although so far there are not many theoretists in this new field in Taiwan, there has been some great progress in the experiments in

Academia Sinica and NCU recently. We hope this group can grow larger and stronger by cooperating with local experimentalist as well as some oversea researchers, like Chii-Dong Lin (UKS, USA), regularly.

II. Activities Summer School: From 8/26 to 8/29 in 2008, we held the 5th AMO summer school in National Taiwan University, locally hosted by Prof. Ying-Chen Cheng in IAMS. This year, we try to include active local members in the four subfields mentioned above to exchange their research results with each other and also introduce the most frontier development to students. We hope this could attract more students to the AMO community and different kinds of research. We will also have a poster session and this should be also a good training program for students and/or postdocs. Local Workshop: On 10/22-10/23 in 2008, we will host a AMO workshop in National Central University. We will invite several top researchers from both local community and those in China to exchange ideas. The goal of this workshop is to provide a flexible forum for domestic physicists to exchange ideas as well as research results with colleagues in China. We believe that it will be a good start for our local AMO researchers to have a broader connection. The workshop will be coordinated by Prof. Tai-Tsong Yi in NCU. International Workshop: We are planning to hold one international workshop in early of 2009 on some specific topics of cold atoms (for example, dipolar atoms/molecules), which are closely related to the interest of local researchers and main string development. So far, we have invited Prof. Eugene Demler (Harvard) and Prof. John Bohn (JILA) to join. We may continue to invite other speakers, say Prof. L. Pitaeviskii. We believe that it can be an important chance for local researchers to be updated with the latest development in cold atoms and/or cold

molecules.

III. Visitors and International Collaborations Visitor in the past year: In the previous year (Sep. 2007-Aug. 2008), we invited Prof. TinLun (Jason) Ho at Ohio State University to visit NCTS from Nov. 18 to 23, 2008. Prof. Tin-Lun Ho is a world-famous condensed matter theorist, and was awarded the Lars Onsager Price 2007 for his great achievement in quantum fluids. During his visit in Taiwan, Prof. Ho had intensive discussions with local researchers in the fields of cold atoms. His visit enables Prof. D.-W. Wang (NTHU) to collaborate with Prof. Ho in the quantum phase transition of condensate in optical lattice. In May 9-18, we also invited Prof. Chris Greene at JILA to visit IAMS, NCU, and NCTS-NTHU. Prof. Greene is a well-known atomic theorist and has contributed three different talks to these three different institutes. Prof. Greene s visit stimulated a closer collaboration of local researchers in different subfield of AMO physics (for example the possible collaboration between Daw-Wei Wang and Chien-Nan Liu on polar molecules in optical lattice). He also gave some valuable comments/suggestions to some local AMO experimentalists. Visitors in the near future: 1) We also have invited Prof. F. Kh. Abdullaev (Physical-Technical Institute, Uzbekistan) to visit NCTS in Oct. 2008. Prof. Abdullaev is a famous researchers on nonlinear physics and Bose-Einstein condensation. He will stay for one month and have a close collaboration with Prof. Tsing-Fu Jiang, Prof. Shih-Chuan Guo, and Prof. Wen-Chin Wu on the dynamical/numerical problems in Bose-Einstein Condensation. 2) Further more, we have invited Prof. John Bohn (JILA) and Prof. Eugene Demler (Harvard) to attend the international workshop on cold atoms/molecules in spring 2009. International collaboration: Our

group

members

have

active


international collaboration with frontier researchers. For example, D.-W. Wang (NTHU) recently has collaboration with Prof. P. Zoller (Innsbruck) on polar molecules, with Prof. T.-L. Ho (Ohio State U.) on the superfluid to Mott insulator transition in optical lattice, and with Prof. E. Demler (Harvard) on dipolar atoms as well as fermions in optical lattice . Prof. Y.-J. Kao (NTU) cooperated with Prof. A. Sandvik (BU) in the development of quantum Monte Carlo calculation. Prof. Chung-Hou Cheng (NCTU) has a close collaboration with Yong Baek Kim (U. Toronto) on the supersolid phase in frustrated system. Prof. T.-K, Fang (FJU) collaborates with Prof. T.-N. Chang (USC) in atomic structure theory. Prof. Chien-Nan Liu (FJU) collaborates with Prof. Shinichi Watanabe and Toru Morishita (University of Electro-Communications, Japan) on the dynamics of Bose-Einstein condensation.

IV. Highlight of Research Results Strongly interacting cold atoms/molecules: A. Exotic quantum phases of polar molecules: D.-W. Wang cooperated with P. Zoller s group on the development of dipolar lattice using polar molecules [1]. They proposed a possible system to replace optical lattice by using the low-dimensional dipolar lattice as a hosted lattice structure. Prof. Wang also developed a complete effective many-body theory for strongly interacting polar molecules [2], and predicted some novel properties in 2D and 3D geometry. This result is beyond the traditionally used Born approximation and can be very relevant for the study of cold polar molecules in the experimental regime. Finally, Prof. Wang and Prof. Pochung Chen (NTHU) found a universal spin decoherence mechanism [3] in a nuclear spin bath, which is important to the semi-conductor-based quantum computation and can be also applied to the study of the dynamics of spinful cold atom mixtures. B. Superfluidity of mixtures of two different fermions: Sungkit Yip, Shin-Tza Wu and Chien-Hua Pao study the dilute fermion gas with pairing between two species and


unequal concentrations in a harmonic trap using the mean field theory and the local density approximation [4]. This is one of the most frontier research directions in the cold atom field. They found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger then certain critical value which increases from the weak-coupling BCS region to the strong-coupling BEC side. In the strong coupling BEC regime, the radii of superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. C. Supersolid phase in triangular lattice: Chung-Hou Cheng and his collaborators, explore supersolid state, an exciting research topic in following years, by applying the Variational Monte-Carlo, the Quantum Monte-Carlo approaches combined with the many-body Green's function techniques on a triangular optical lattice [5]. Special focus is on the noise correlations in boson density which has been proven a useful probe to this phase via time of flight measurement of condensed bosons. This is an important measurable quantity to probe the many-body state in the traped bosons. Weakly interacting bosonic atoms: Shih-Chuan Guo and his collaborators have found a new prototype of quatnum turbulence in trapped BEC via the disruption of a single quantized vortex ring [6,7]. This quantum turbulence is well characterized by an energy spectrum following the famous Kolmogorov's -5/3 power law in classical turbulence. They also have ascertained that the quantum turbulence occuring in a 2D BEC is simultaneously characterized by Kolmlgorov's -5/3 power law and Kraichnan's -3 power law in the energy spectrum - a very unique feature that belogns to the 2D classical turbulence. Currently, they are examining the energy spectrum for quantum turbulence achieved by various combinations of system parameters. Atomic structure and spectroscopy: Recently, by using a B-spline-based

complex rotation (BSCR) method, Te-Kuai Fang, Tu-Nan Chang (USC) and their collaborators have successfully included the spin-orbit interaction for the study of atomic photoionization leading to multiple ionization channels dominated by doubly excited resonances for two-electron and divalent atoms. Its application to Mg photoionization gave good agreement between the theoretical and the observed singlet-triplet mixed Mg spectra [8]. They also have applied the BSCR method to investigate the ground-state photoionization for Ca and Sr atoms, where more overlapped resonance structures are expected due to a stronger spin-mixing.

[4]

[5]

[6]

V. References [1] G. Pupillo, A. Griessner, A. Micheli, M. Ortner, D.-W. Wang, and P. Zoller, Cold Atoms and Molecules in Self-Assembled Dipolar Lattices, Phys. Rev. Lett. 100, 050402 (2008). [2] D.-W. Wang, An effective theory of strongly interacting polar molecules, New J. Phys. 10, 053005 (2008). [3] Yi-Ya Tian, Pochung Chen, and D.-W. Wang, Universal Dynamics of Electron

[7]

[8]

Spin Decoherence in a Nuclear Spin Bath, Phys. Rev. B, 77, 174434 (2008). C.-H. Pao, Shin-Tza Wu, and Sungkit Yip, Asymmetric Fermi superfluid with different atomic species in a harmonic trap, Phys. Rev. A 76, 053621 (2007). Sergei Isokov, Shiuan-je Shiu, Jian-Jeng Wu, Young-Chung Chen, Chung-Hou Chung, Yong Baek Kim, Krishnendu Sengupta, Quasi-imcommensurate supersolid phase in the Bose-Hubbard model on an anisotropic lattice, ArXiv:0708.3084 (submitted to Physical Review Letters). C.-H. Hsueh, S.-C. Gou, T.-L. Horng and Y.-M. Kao, Vortex-ring solutions of GrossPitaevskii equation for an axisymmetrically trapped Bose-Einstein condensate, J. Phys. B: At. Mol. Opt. Phys. 40, 4561 (2007). T.-L. Horng, C.-H. Hsueh and S.-C. Gou, Transition to quantum turbulence in BoseEinstein condensate through bending-wave instability of a single vortex ring, Physical Review A 77, 063625 (2008). T. K. Fang and T. N. Chang, B-splinebased complex-rotation method with spindependent interaction, Phys. Rev. A 76, 012721 (2007).


Focus Group on Quantum Information Science Coordinators: Yueh-Nan Chen (National Cheng Kung University; email: [email protected]) Hsi-Sheng Goan (National Taiwan University; email: [email protected]) Committee members: Alec Maassen van den Brink (Academia Sinica), Yia-Chung Chang (Academia Sinica), Pochung Chen (National Tsing Hua University), Chi-Yee Cheung (Academia Sinica), Chung-Hsien Chou (National Taiwan University), Li-Yi Hsu (Chung Yuan Christian University ), Chopin Soo (National Cheng Kung University), Zheng-Yao Su (National Center for High-Performance Computing), Wei-Min Zhang (National Cheng Kung University)


he main mission of the QIS focus group is to build a platform of communication and discussion for researchers in this area in Taiwan. In the last few years, we have brought QIS researchers in Taiwan to work and discuss research together and to hold activities, such as scientific seminars, workshops and short-term schools. We have also been seeking to establish links and exchanges as well as to initiate collaborations with other QIS researchers worldwide. Focused research topics: Quantum decoherence, quantum measurement, quantum entanglement and communication.

II. Activities and Beneficiaries Activities 1. Winter school on, "The 3rd Winter School on Quantum Information Science" at Taitung, Jan. 5 ~ 7 (2008). 2. "The 2nd International Workshop on SolidState Quantum Computing and Mini-School on Quantum Information Science" at NTU, June 23 ~ 27 (2008). 3. Mini-workshops and seminars at NCKU, NTHU, and NTU. Beneficiaries 1. To enhance international visibility and


benefit the QIS community in Taiwan, we have held "The 2nd International Workshop on Solid-State Quantum Computing and Mini-School on Quantum Information Science" in Taipei during June 23 ~ 28 (2008). Many world-leading researchers, such as Prof. Milburn, Prof. Martinis, Prof. Nori, Prof. Schoen, Prof. Delsing, and Prof. Tarucha …, were invited to give lectures. The workshop attracted many participants, including faculties, postdocs and students. The Proceedings of the workshop and minischool will be published by the International Conference Proceedings Series of the American Institute of Physics (AIP; http://proceedings.aip.org). The printed Proceeding book and its online version will have the Volume number in the AIP Conference Proceedings Series, ISSN and ISBN, and will be registered at the Library of Congress. The proceedings are valuable as topical status reports providing quick access to information before it appears in the traditional journal literature. 2. Ever since Prof. B. L. Hu (Univ. of Maryland) became the senior multi-year visitor of our focus group, one of the major QIS focus group research topics was focused on the field of quantum decoherence. The 2008 winter school was the third summer school (the previous two were held in 2006 and 2007) focusing on this particular topic. As a result of these schools, several focus group members have engaged in the research on Non-Markovian dynamics of qubits and continuous variable

systems in external environments. 3. We also successfully attracted young researchers into this field, such as the postdoctoral fellow (Dr. Che-Ming Lee) and graduate students (Mr. W. Y. Tu, Mr. H. B. Chen, Mr. D.B. Tsai, Mr. C.H Li and Mr. Y.Y. Lai). Training of young-generation physicists 1. Inviting potential young-generation physicists as speakers at mini-workshop (1) Dr. Tzu-Chieh Wei (Institute for Quantum Computing, Univ. of Waterloo) (2) Dr. Min-Hsiu Hsieh (Univ. of Southern California, USA)

III. Visitors and International Collaborations Visitors 1. Prof. B. L. Hu, Univ. of Maryland, USA (July 2008) 2. Prof. Gurvitz, Weizmann Institute (Nov. 6, 2007 ~Feb. 5, 2008) 3. Prof. Daniel Braun, Universite Paul Sabatier, France (Jan. 2 ~7, 2008) 4. Prof. Xin-Qi Li, Chinese Academy of Sciences (Dec. 27, 2007 ~Jan. 29, 2008) 5. Dr. Jacob Taylor, Massachusetts Institute of Technology (Jan. 4 ~ 8, 2008) International Collaborations 1. Prof. T. Brandes at Technische Universität Berlin, Germany -- A three-year international collaboration project with Prof. Y. N. Chen. 2. Prof. G. J. Milburn at the University of Queensland and Prof. Xin-Qi Li at the Chinese Academy of Science -- with Prof. H.-S. Goan on quantum measurement and quantum feedback control of qubits and continuous variable systems.

IV. Highlights of Research Results

I. Decoherence 1. Induced decoherence by interacting quantum spin baths: We study the reduced dynamics of a single or two qubits coupled to interacting quantum spin baths described by a one-dimensional XXZ Heisenberg Hamiltonian. By using timedependent density matrix renormalization group (TD-DMRG) technology we go beyond the uniform coupling central spin model and evaluate nonperturbatively the induced decoherence and entanglement [1]. 2. Universal dynamics of quantum spin relaxation in a spin bath: We investigate the universal spin relaxation dynamics of a localized electron due to hyperfine interaction with nuclear spins. We prove that (1) the electron spin relaxation dynamics can always show universal behavior if the initial state is composed of sufficient large amount of spin eigenstates. (2) For a given system, the pattern of the universal dynamics is governed by a single initial parameter [2]. 3. Quantum Decoherence of Coupled Oscillators in a General Environment We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice) and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (``sudden death"). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times [3,4]. 4. Decoherence of a qubit embedded inside a suspended phonon cavity We elucidate the theory of phonon-induced decoherence of a double dot charge qubit that is embedded inside a suspended semiconductor slab. The influences of the lattice temperature, width of the slab, and positions of the dots on the decoherence are analyzed. The decoherence is markedly suppressed by the


inhibition of the electron-phonon coupling [5]. II. Quantum measurement 1. Shot-noise spectrums of non-Markovian QD excitons We propose to detect non-Markovian decay of an exciton qubit coupled to multi-mode bosonic reservoir via shot-noise measurements. Non-equilibrium current noise is calculated for a quantum dot embedded inside a p-i-n junction [6]. We also propose to observe the retardation effect between two quantum dots (via current-noise) in a onedimensional waveguide [7].

III. Quantum Computation 1. Charge-to-spin conversion of electron entangled states and spin interaction free solid-state quantum computing: We have proposed an implementation of scalable spin quantum computation in semiconductor nanostructure without resorting to spin-spin interaction. [8] We can generate a charge entangled state of two electrons using single electron transition assisted by a semiconductor multiple-quantum-dot structure.

IV. Quantum entanglement and communication 1. Generalized Smolin states and their applications We consider the generalized Smolin states with common stabilizers among the mixtures [9]. In particular, we focus on the family of the mixed states that maximally violate Bell-type inequalities. The Bell-correlated mixed states can be exploited in the scheme of remote onequbit information concentration [10]. 2. Entanglement detection and witness We propose the "correlator" as the product of the two differences of joint probabilities [11]. A necessary condition of quantum correlation is proposed. The correlators help construct the entanglement witness and Belltype inequalities. 3. Quantum bit commitment with secret parameters


The proof of the no-go theorem of unconditionally secure quantum bit commitment assumes that the parties involved know every detail of the protocol so that no secret parameters exist. We extend the theorem to cover the cases in which secret parameters (secret probabilities) are allowed [12]. 4. Minimal classical communication and measurement complexity for quantum information splitting We present two quantum information splitting schemes [13] using respectively tripartite GHZ and asymmetric W states as quantum channels. We show that if the secret state is chosen from a special ensemble and is known to the sender (Alice), then she can split and distribute it to the receivers Bob and Charlie by performing only a single-qubit measurement and broadcasting a one-bit classical message. No other schemes could possibly achieve the same goal with simpler measurement and less classical communication.

V. References [1] Cheng-Yan Lai and Jo-Tzu Hung and Chung-Yu Mou and Pochung Chen, Phys. Rev. B 77, 205419 (2008). [2] Yi-Ya Tian, Pochung Chen, and Daw-Wei Wang, Phys. Rev. B 77, 174434 (2008). [3] Chung-Hsien Chou, B.L. Hu, and Ting Yu, Physica A 387, 432-444 (2008). [4] Chung-Hsien Chou, Ting Yu, and Bei-Lok Hu, Phys. Rev. E 77, 011112 (2008). [5] Y. Y. Liao, Y. N. Chen, W. C. Chou, and D. S. Chuu. Phys. Rev. B. 77, 033303 (2008). [6] Y. N. Chen and G. Y. Chen, Phys. Rev. B 77, 035312 (2008). [7] Yueh-Nan Chen and Lukas Gilz, Appl. Phys. Lett., accepted (2008). [8] Wei-Min Zhang, Yin-Zhong Wu, Chopin Soo, and Mang Feng, Phys. Rev. B 76, 165311 (2007).

[9] Li-Yi Hsu, Phys, Rev. A 76, 022322 (2007). [10] Li-Yi Hsu, Phys, Rev. A 76, 032311 (2007). [11] C. M. Li, L. Y. Hsu, Y. N. Chen, D. S. Chuu, and T. Brandes, Phys, Rev. A 76, 032313 (2007). [12] C.-Y. Cheung, Int. J. Mod. Phys. B 21, 4271 (2007).

[13] Z.J. Zhang and C.-Y. Cheung, J. Phys. B 41, 015503 (2008). [14] X. Z. Yuan, K. D. Zhu and H.-S. Goan, Eur. Phys. J. D 46, 375 (2008) [15] T.-Y. Huang, C.-T. Liang, G.-H. Kim, C. F. Huang, C.-P. Huang, J.-Y. Lin, H.-S, Goan, and D.A. Ritchie, accepted by Phys. Rev. B (2008).


Highlights of Programs Working Group on Plasma Science Coordinator: Kuan-Ren Chen (National Cheng Kung University; email: [email protected]) Committee members: Lin-Ni Hau (National Central University), Jang-Yu Hsu(National Cheng Kung University), Chwung-Shan Kou (National Tsing Hua University), Wei-Chi Liu (National Taiwan Normal University), JyhPyng Wang (Academia Sinica)


beyond national boundaries. 3. Incubating young generations of plasma scientists.

he NCTS Plasma Science Program identifies the following plasma research frontiers: space and astrophysical plasma, fusion plasma, laser plasma, surface plasma, coherent radiation, plasma applications, low temperature plasma, and gluon plasma. The local community has research activities in all but the last one. In fact, it has world-leading research result in almost every area, although the size of local plasma physics community is still small. Education is essential for this community to increase its enabled manpower and future prosperity. Plasma researches are often across disciplinary boundaries and important in both scientific frontiers and critical applications. The NCTS Plasma Science Program provides a forum for the local plasma science community, to achieve the following objectives, and to operate under the guidelines listed below. I. 1. Objectives: 1. Promoting theoretical plasma research in Taiwan. 2. Stimulating research collaborations with experimentalists, of inter-disciplinary, and


I. 2. Guidelines: 1. Following the NCTS written guidelines. 2. Providing the needed administrative assistances and a flexible and reliable service for easy budget access. 3. The NCTS budget should be used efficiently. 4. Suggestions for activities and positions are encouraged. 5. Proposal and report in written should be brief; in most cases, an email may be enough as long as key information and justifications included. 6. The program committee makes the decision only based on the objectives, the guidelines, the academic merit, and available budget. 7. Activities aiming to stimulating collaboration and interaction are encouraged and have a higher priority for budget supporting. 8. Activities aiming to incubating young generations are encouraged and have a higher priority for budget supporting. 9. Sponsored foreign visitors should be superior in particular methodology and knowledge. 10. Local experts and groups are encouraged to offer tutorial courses, schools, and workshops. 11. Self-organized working groups across institutions are encouraged. 12. Each working group should have focused interest and activities, and is encouraged to be bounded with specific experimental concerns. 13. The

plasma sub-areas and working groups are coupled through common interest in simulation and theory, such as nonlinear dynamics. 14. Anyone in the community is welcome to participate in any of the groups of his/her interest.

II. Activities II. 1. Surface Plasma Working Group Meetings Surface plasma on metallic surface is a newest frontier in plasma research. It is a research area of multi-disciplines, involving physics, mathematic, electro-optics, biomedical, electronics, materials, nanotechnology, mechanical, and electrical engineering. This biweekly meeting was organized by Professor Y. C. Lan in 2006, Professor S. J. Chen in 2007 and Professor H. C. Chui in 2008. At the beginning, the active participants include five NCKU professors and one professor with Kaoshiang University of Applied Science and their students. In addition to working group discussion, external and internal speakers are invited. The purpose is to educate students and to stimulate collaboration. In July 2007, NCKU realized the importance of a simulation result by the group. A NCKU experimental team supported by the Top University fund is formed and a joined biweekly meeting is being held. The number of involved professors has been increased to about fifteen. II. 2. Computational Plasmonic NanoPhotonics Meetings At nano scale, charge is the most effective media to interact with photons. Thus, for many experts, plasmonic is the most important area of nano-photonic research. While covering both fundamental physics and applications, this monthly working group meeting aims to understand the interactions of photons and metallic/dielectric structures, and to investigate novel optical phenomena. About two speakers per month are invited for presentation. It is organized by Professors D. P. Tsai of NTU and W. C. Liu of NTNU. The organizers and some of its participants have successfully landed a National Nano Project.

II. 3. 2007 and 2008 Laser-Plasma Interaction Summer School II. 3. A. Purpose In Taiwan and possibly many other places in Asia, it is not uncommon to meet a prospective graduate student who is interested in experimental sciences but poorly prepared for laboratory work. Many students can do textbook exercises well, but do not know how to describe the thread of a screw, or how to read the color code of a resister. They cannot operate a milling machine or a soldering iron, or tell the difference between epoxy and silicon rubber. The reason is simple: these are not part of their education or experience. In this summer school held at National Taiwan University by Jyhping Wang of Academic Sinica from July 16 to 20 of 2007 and from July 7 to 11 of 2008, respectively, we wish to extend their education in this direction, even though it is not possible to provide them a real laboratory experience. II. 3. B. Courses Forty hours of lectures that form fourteen courses were delivered. The objective is to introduce to the participating students a near complete set of basic knowledge that is required in a laser-plasma laboratory. In addition, recognizing computer simulation as a form of numerical experiments, the courses also cover basic knowledge of computer simulation. The courses are: characteristics and applications of optical components, ultrafast optics and high-power lasers, basic laserplasma interaction, experimental techniques in laser-plasma interaction, basic numerical simulation, Particle-in-cell simulation, handy computation: Introduction to Matlab, Mathematica, and Mathcad, working with electronics, computer control of instruments, introduction to electro-optics instruments, working with vacuum, data analysis and curve fitting, mechanical design and drafting, data plotting and presentation, and using LaTeX for preparing scientific documents. II. 3. C. Participation There were 160 and 130 participants enrolled in year 2007 and 2008, respectively.


In additional to a few faculties and some fulltime research assistants, most of them are master students, undergraduate students, and Ph.D. students. At the end, we had conducted a poll to see how students evaluate the courses. In the poll we asked students to rate each course in two scales, one on the level of difficulty and the other on the pace of lecturing. The cost per participant is about 1,500NT for this five days intensive school. II. 4. Particle-in-cell Mini-school Particle-in-cell is a first-principle and the most powerful method to simulate plasmas. Aiming to educate students and young plasma scientists in a joined effort, this mini-school brings local experts together. It was organized by Professor Y. C. Lan and was held at NCKU on September 29 and 30, 2007. There were about 50 participants including graduate students, postdocs and a few professors. II. 5. International Workshop on EM Particle-In-Cell Simulation of Plasmas The Workshop was held at Fu Jen Catholic University during January 5-6, 2008. We specially invited the foreign researchers from the Plasma Theory and Simulation Group at University of California, Berkeley. The focus of this workshop was the electromagnetic particle-in-cell simulation of plasmas and it's applications, from fundamental studies to device applications. The purposes of this workshop are the following. The first is to get together local and foreign researchers to discuss the EM PIC method. The second aims to foster new collaborations between theorists and experimentalists as well as between local researchers and foreign visitors. The last, but not the least, is to attract young generation into this revival field, plasmas, to provide them with the opportunities to discuss with each other and with foreign researchers. The workshop is sponsored by National Science Council and Fu Jen Catholic University while the Program provides administrative help and some expenses for the need of local participants. II. 6. The 2007 NCTS Plasma Science Workshop

The Workshop was a community-wide event and was held at the National Cheng Kung University during December 22-23, 2007. The Workshop was organized by Professor Frank C. Z. Cheng and is sponsored by the NCTS, Plasma and Space Science Center (PSSC) and Department of Physics of National Cheng Kung University and cosponsored by Tung Sheng Chang Foundation of Culture and Education. All plasma science areas, from fundamental studies to device applications, are covered. The workshop served as a forum to promote plasma sciences, exchange ideas, foster collaborations, and encourage student participation. There were three plenary talks, sixteen invited talks, as well as some oral and poster presentations. There were about 70 participants. II. 7. A Short Course on Magnetohydrodynamics (MHD)

the

As a fluid method describing plasma, MHD is a common methodology in plasma science. This two days short course is organized by Professor L. N. Hau and J. Y. Hsu, and will be held at NCKU on August 28 and 29, 2008. Beginning with an introduction and equilibrium, this short course covers the linear theory of wave and instability, the nonlinear theory on shock waves, statistics approach, bifurcation and boundary layer problem, as well as computational MHD. The number of seats was set as forty-five and was filled quickly. II. 8. The International Workshop on Frontiers In Space and Fusion Energy Sciences (FISFES) The International Workshop will be held at the National Cheng Kung University during November 6-8, 2008. It is organized by Professor Frank C. Z. Cheng and sponsored by the Plasma and Space Science Center of National Cheng Kung University and the NCTS. About fourteen speakers from USA, Japan, Korea and Canada are invited, in additional to a few from Taiwan.

III. Visitors and International Collaborations III. 1. Professor Liu Chen, UC Irvine, USA


Professor Liu Chen has been a frequent visitor. He officially visited NCTS from 11/826, 2006. He spent the first week in NCU, the second week in NCKU, and then in NDHU and NCU. In addition to giving series lectures on gyrokinetic theory and toroidal physics, he started the collaboration on the work of relativistic ion cyclotron instability under nonuniform magnetic field with Professor K. R. Chen and his student, Mr. T. H. Tsai. After the visit, Mr. Tsai went to UC Irvine from the end of March 2007 to January 2008 to carry out the theoretical derivation, under the support of National Science Council. During the meantime, Professor Liu Chen has visited Taiwan twice (one in July and the other in September) and discussed with Professor K. R. Chen, under the support of NCU with a Chair Professorship; the three got together for indepth discussion in November 2008 during the annual meeting of Plasma Physics Division of American Physical Society, held at Orlando, FL, USA. The discussion continues after Mr. Tsai returned; e.g., Professor Liu Chen visited us again in March 2008. The result yielded is consistent qualitatively with Particle-in-cell simulation; the quantitative comparison has been done. Two papers are being written.

systems. The spheromak plasma equilibrium paper while submitted to APS meeting still needs further effort to finish, however. III. 3. International Speakers of the International Workshop on Frontiers In Space and Fusion Energy Sciences (FISFES) Daniel N. Baker (University of Colorado at Boulder, USA), Masaki Fujimoto (ISAS/JAXA, Japan), Masafumi Hirahara (University of Tokyo, Japan), Mitsuru Kikuchi (Japan Atomic Energy Agency, Japan), GyungSu Lee (National Fusion Research Institute, Korea), Robert P. Lin (University of California at Berkeley, USA), Neville C. Luhmann, Jr. (University of California at Davis, USA), Atsushi Mase (Kyushu University, Japan), Yasushi Ono (University of Tokyo, Japan), Hyeon Park (Pohang University of Science and Technology, Korea), Shigeru Sudo (National Institute for Fusion Sciences, Japan), William M. Tang (Princeton Plasma Physics Laboratory, USA) James W. Van Dam (University of Texas at Austin, USA), Andrew W. Yau (University of Calgary, Canada). The cost will be covered by the NCKU Plasma and Space Science Center.

III. 2. Professor C. M. Ryu, Postech, Korea

IV. Highlights of Research Results

Professor C. M. Ryu visited NCTS from 6/26 to 7/8, 2007. He is a well rounded plasma physicist and has done research in various areas of plasma physics. He made presentations on "Magnetic Field Generated by Transport Flow" at both NCKU and NCU. During the visit, he started collaborative work with Professor J. Y. Hsu on the spheromak plasma equilibrium. He pointed out the correlation dimension to quantify the fractal dimension and one student has implemented a numerical code successfully to examine for example the Henon map, and will apply the same to arc root dynamics, and other stochastic

Taiwan's plasma physics community is relatively small in size as compared with other research fields of physics. However, the academic performance is impressive with so many outstanding research results and the international reputation is high. For example, in the areas of electron cyclotron maser, dusty plasmas, space plasma, laser plasma, redSprite observation, fast ion cyclotron instabilities, and recently surface plasma, Taiwan's groups are making outstanding original contributions and, in fact, are among leaders of the international research community.


Working Group on Softmatter and Nonlinear Physics A. Nonlinear Phenomena in Physical and Biological Systems Coordinators: Mingchih Shih (National Chung Hsing University; email: [email protected]) Committee members: Chao-Nien Chen (National Changhua University of Education), Kai-Jung Chi (National Chung Hsing University), Tzyy-Leng Horng (Feng Chia University), Sy-Sang Liaw (National Chung Hsing University), Jiunn-Ren Roan (National Chung Hsing University)

I. Introduction

II. Activities (1) Regular meeting

he working group includes several faculty members and Ph. D students from various institutes in central Taiwan. The key members of this working group are: SySang Liaw(Physics, NCHU); Jiunn-Ren Roan(Physics, NCHU); Kai-Jung Chi(Physics, NCHU); Ming-Chih Shih(Physics, NCHU); IMin Tso(Life Science, THU); Chao-Nien Chen (Math, NCUE); Chung-Tu Yang(Entomology, NCHU); Tzyy-Leng Horng(Applied Math, FCU). The main theme of the group focuses on the non-linear phenomena that appear in nature, including the biological world. Our activities include regular meetings, workshops, and short visits from or to institutes abroad. Current projects under intensified discussion comprise: 1. The mechanical responses of spider web (Biological Materials) 2. Fluid dynamics of biological sniffers (Fluid Mechanics) 3. The effect of Pterostigma on insect locomotion (Biomechanics) 4. The mechanism of the Brazil nut effect and its reverse (Granular Physics); 5. Biological patterns and stability of the Turing equation (Pattern Formation); 6. Statistical behavior of agents in economics (Econophysics). Because of the interdisciplinary nature of our topics, we constantly consult with experts from economics and biology departments.


Biophysical Journal Club (BJC): Thursday 12:00-13:00 Biophysical Journal Club was initiated by Prof. Roan since 2004, and it has been continues and thriving successfully with the support of this focus group. BJC is well organized and has attracted broad attendance from various disciplines. The mailing list of BJC continues growing. About 20 to 40 people attend the Club at each gathering. Details of the BJC activity subjects can be found at http://140.120.11.15/vedio/biophysics/Chinese/ journal%20club/activity.htm Nonlinear phenomena seminar: Monday 12:00-13:00 Nonlinear phenomena seminar was organized by Prof. Liaw. The scope of the seminar includes granular physics, pattern formation and econophysics. About 10 to 15 people attend the seminar at each gathering. (2) Workshops • Biophysics workshop: Biological materials and Animal Behaviors, Hsin-Hua Forest Station, Tai-Nan, Sep. 5-7, 2008 We focus on the physics of biological materials and animal behaviors in this workshop. Five prestigious speakers are invited: Kai-Jung Chi (Physics, NCHU); I-Min Tso (Life Science, THU); Chung-Tu Yang (Entomology, NCHU); Tzen-Yuh Chiang (Life Science, NCKU) and Hsin-Drow Huang (NMNS) will give lectures in this workshop. Students and Post Docs are also encouraged to contribute. The audience is expected to about 50 people.

• Biophysics workshop: Surface and interface physics of biological systems, Huisun Forest Station, Nautou, Oct 31 ~ Nov 2 (or Nov. 79), 2008 The second workshop of biophysics will focus on the physics of surface and interface properties in biological systems. The main speaker will be Dr. Stanislav Gorb from MaxPlanck Institute. Dr. Gorb will give a serie of lectures in the workshop. The audience is expected to about 60 people. (3) Conferences Under the support of this focus group, we have sent student to attend international conferences: • R.T. Liu, J.Y. Wang, F.F. Chung, Hangzhou and Jinhua, China, 11/12-15, 2007 The 3rd Cross-strait conference on statistical physics. Oral and poster presentations.

III. International collaborations 1. Physics of Biological surfaces: Chi, Shih, Gorb Prof. Chi has great experience on the mechanical properties of biological systems, and she invites Prof. S. Gorb who is the group leader of evolutionary biomaterials group at the Max-Planck-Institute for a series of biophysics workshop. Together, they tend to explore the feasibility of study physical properties of biological surfaces. 2. Biological pattern formation: Liaw, Liu, Maini During the execution of this focus group, Professor S.S. Liaw and Dr. Ruey-Tarng Liu of NCHU had established a steady research relationship with Professor P.K. Maini in Oxford. One of the great successes in their collaboration is the joint publication which has

been highlighted by Nature magazine in 2006. Their following research work on the oscillatory Turing pattern has also been published in 2007. Their work on the biological pattern formations is continued. 3. Sand flow through a vertical pipe: Liaw, Liu, Shih, Matsushita The experiment was proposed by Prof. Matsushita of Chuo University during his visit to our group in September, 2005. We set up the experiment immediately and have observed many interesting phenomena since then. We are constructing a model to simulate the density flow of the sand in the pipe, and to analyze its power law.

IV. Highlights of research results 1. In the study related to econophysics, Prof. Liaw used agent-based simulation on the model of the Minority Game and found some implications about where does the power law come from in complex systems. 2. The Brazil nut effect in granular physics has puzzled physicists for more than 50 years. After three years of intense study, Fei-Fang Chung et al have come up with a mechanism that successfully describes a type of horizontal segregation phenomenon very similar to the Brazil nut effect. They are optimistic in solving the long-standing puzzle in the coming years.

V. Selected Publications [1] Sy-Sang Liaw, "Frequency distributions of complex systems", J. Stat. Mech. P05015 (2008). [2] Fei Fang Chung, Sy-Sang Liaw*, and Chia-Yi Ju, "Spiral trajectories in the horizontal Brazil nut effect", Phys. Rev. E 77, 061304 (2008).


Working Group on Softmatter and Nonlinear Physics B. Soft-matter, Biophysics & Systems Biology Coordinators: Peilong Chen (National Central University; email: [email protected]), Hoong-Chien Lee (National Central University; email: [email protected]) Committee members: Cheng-Hung Chang (National Chiao-Tung University & National Center for Theoretical Sciences), Chi-Ming Chen (National Taiwan Normal University), Hsien-Da Huang (National Chiao-Tung University), Hsueh-Fen Juan (National Taiwan University), Chun-Yi David Lu (National Taiwan University), Ann-Pin Tsou (National Yang- Ming University)


he working group of soft-matters, biophysics and systems biology (SBSB) was running from 2006 after combining two previously related focus groups. The SBSB working group contains participants from diversified fields, especially with many more biology background researchers. Academic activities have increased appreciably, especially for workshops and seminars. In the past year, we have organized a number of activities to promote collaborations both within Taiwan and internationally. Our purpose is to encourage the use of theoretical means to investigate the fundamental principles in softmatter and bio-related sciences and aiming at obtaining some quantitative understanding in soft materials and biological processes with emphasis on the more recent hot topics using systems approaches to investigate biological systems. Emphasis is also put on the communications and collaborations with experimentalists, as reflected by the fact that some of the active members of the are experimentalists also. In recent years, we have encouraged strongly on creating actual collaboration environment between our local members and researchers in the Asian-Pacific regions and we are starting to see some concrete outcomes. SBSB working group also organizes regular and irregularly scheduled seminars, workshops, conferences on soft-matter


physics, biophysics and systems biology held at various associated institutions. We have been organizing the weekly "Soft-Bio Matters Seminar/Journal Club" for more than 5 years, at NCU. This active seminar series has been inviting local and foreign visiting researchers on various areas of soft-matter and biophysics and it turns out that various research ideas and actual collaborations are indeed come out as direct/indirect consequences of this seminar series. In the past year, some topics are more emphasized in the areas of DNA conformations, genomic/protenomic analysis, evolution theory, nonequilibrium physics in pulling biomolecular bonds, polyelectrolytes; rheology & pattern formation in complex fluids; excitable bio-systems such as cardiac and neural biophysics; collective motions in active organisms; membrane biophysics; dynamics on complex and bio networks; Brain physics; physics of DNA & proteins, etc. SBSB working group also supported a number of foreign visiting scientists aiming at academic interflow of ideas and set up collaborations. We have both short and longterm visitors, delivering lectures and carrying out collaborations. Foreign visitors in the past year include: Prof. Moira L. Styen-Ross (University of Waikato), Prof. D. Alistair Styen-Ross (University of Waikato), Prof. Takao Otha (Kyoto University), Prof. Yohannes Shiferaw (California State University at Northridge), Dr. Qiuming Yu (University of Washington), Dr. Kuo-Ping Chiu (Genome Institute of Singapore), Dr. Chia Lin Wei (Genome Institute of Singapore), Prof. Tony Zee (UC

Santa Barbara), Prof. Daniel Figeys (University of Ottawa), Prof. Shao-Chen Lee (Sunnybrook Health Science Center), Prof. Rong-San Huang (Saint Louis University), Dr. Kuan Wang (NIH), Dr. Chia Lin Wei (Genome Institute of Singapore), Dr. Hsinyi Steve Tsang (Johns Hopkines), Dr. Kuan Wang (National Institute of Arthritis and Musculoskeletal and skin Diseases), Prof. Sangsoo Kim (Korea Res. Inst. Of Biosci. & Biotech).

II. Activities Continuing our activities from the past year, we organized a number of workshop and schools. We have attracted a number of young and established local researchers, as well as participants from nearby countries. It is worth to mention that these workshop/conferences always attract a good collection of active researchers from various local institutions to participate/organize these activities in an active way.

Biophysics Camp 2007

1. Mini Workshop on Mass Spectrometrybased Proteomics (NCU), Aug. 8, 2007. 2. Biophysics Camp 2007 (NCU), Oct. 27–28, 2007

Mini-Workshop on Neuroscience

3. Mini-Workshop on Neuroscience (NCU), Dec. 10, 2007 4. Biophysics & Soft-Matter Days 2008 (NCNU), Jan. 21-24, 2008 5. Mini-Workshop on soft matters (NCU), Feb. 19, 2008 6. The 19th Complex Systems Symposium (NCU), May 17-18, 2008 We have long been putting special focus on attracting/promoting students to enter into our field by organizing the Biophysics Camp. The response was very positive. Continuing our tradition, the 19 th Complex Systems Symposium was formatted to have speakers consisted of solely graduate students. In this two-day symposium, graduate students from various institutions reported their concrete research results. The best two talks given by xxx titled xxx and by xxx titled xxx were awarded with best presentation awards. Students found this to be very stimulating and the positive competition among the students transformed into an enthusiastic atmosphere.

BioPhysics & Soft-Matter Days 2008

Mini-Workshop on soft matters (NCU)


III. Highlights and Research Results In the paper entitled Bell's expression and generalized Garg's form for forced dissociation of a biomolecular complex [5], it is shown that the celebrated Bell expression provides a good approximation for the bond dissociation rate of a biomolecular complex under constant force. In the paper Contactinduced structure transformation in transmembrane prion propagation [6], a theoretical model for the molecular mechanism of the transmission of prion diseases due to a particular transmembrane form is proposed and computer simulation results are obtained. In the paper The Rubik's cube problem revisited: a statistical thermodynamic approach [13], the protein folding problem is studied by observing the thermodynamic and kinetic behavior of a Rubik's cube model. In the paper Characterization of microRNARegulated Protein-Protein Interaction Network [16] the topological analysis of global correlation between microRNA regulation and protein-protein interaction network shows that target genes of individual microRNA tend to be hubs and bottlenecks in the network.

V. Related Recent Selected Publications * The below publications are direct or indirect outcomes of the activities organized by our focus group. However, not all of these publications have shown affiliation with NCTS.

[1] Polymer Turbulent Drag Reduction near the Theta-Point, S.T. Lim, C. A. Kim, H.J. Choi , Pik-Yin Lai, and C.K. Chan, Europhys.. Lett. 80, 58003 (2007) [2] Spherical vesicles distorted by a grafted latex bead: An exact solution, J. Benoit and A. Saxena, Phys. Rev. E 76, 041912 (2007) [3] Lifetime of ligand-receptor clusters under external force, Yi-Ping Chu, Chih-ChaoTang, and Hsuan-Yi Chen, Physical Review E, 76,061905 (2007) [4] Influences of Linkage Stiffness on Rupture Rate in Single-Molecule Pulling Experiments, Han-Jou Lin, Yu-Jane Sheng, Hsuan-Yi Chen, and Heng-Kwong Tsao, J. Phys. Chem. B, 111, 6493 (2007)


[5] Bell's expression and generalized Garg's form for forced dissociation of a biomolecular complex, Han-Jou Lin, Hsuan-Yi Chen, Yu-Jane Sheng, and Heng-Kwong Tsao, Phys. Rev. Lett., 98, 088304 (2007) [6] Contact-induced structure transformation in transmembrane prion propagation, D.M. Ou, C.-C. Chen, and C.-M. Chen, Biophys. J. 92, 2704 (2007) [7] Driven polymer transport through a nanopore controlled by a rotating electric field: Off-lattice computer simulations, Y.S. Tsai and C.-M. Chen, J. Chem. Phys., 126, 144910. (2007) [8] The dielectric spectrum of flexible polyelectrolyte solutions, C.-Y.D. Lu, Europhysics Letters 80, 67002 (2007) [9] Ganoderma lucidum polysaccharides in human monocytic leukemia cells: from gene expression to network construction, Cheng, K.-C., Huang, H.-C., Chen, J.-H., Hsu, J.-W., Cheng, H.-C., Ou, C.-H., Yang, W.-B., Chen, S.-T., Wong, C.-H., Juan, H.F., BMC Genomics 8, 411 (2007) [10] A statistical simulation approach for early stage thin-film growth from vapordeposited atoms, Peilong Chen, T. Y. Wang and M. F. Luo, Journal of Chemical Physics 127, 144714 (2007). [11] Field-induced columnar structures in a quasi-two-dimensional system of dipolar particles, Shin-Shing Yeh, Ching Hsueh, Peilong Chen and Jorge Vinals, Physical Review E 76, 051407 (2007). [12] Elasticity and stability of a helical filament with spontaneous curvatures and isotropic bending rigidity, Zhou, Z; Joos, B; Pik-Yin Lai; Young, YS; Jan, JH, Mod. Phys. Lett. B 21, p.1895-1913 (2008) [13] The Rubik's cube problem revisited: a statistical thermodynamic approach, ChiLun Lee and Mu-Chieh Huang, Eur. Phys. J. B 64, 257 (2008) [14] Forced dissociation of a biomolecular complex under periodic and correlated random forcing, Han-Jou Lin, Yu-Jane Sheng, Hsuan-Yi Chen, and Heng-

Kwong Tsao, J. Chem. Phys., 128, 084708 (2008) [15] Non-linear rheology of lamellar liquid crystals, C.-Y.D. Lu, P. Chen, Y. Ishii, S. Komura, and T. Kato Eur. Phys. J. E 25, 91 (2008) [16] Characterization of microRNA-Regulated Protein-Protein Interaction Network,

Hsu, C.-W., Juan, H.-F., Huang, H.-C. Proteomics 8, 1975-1979 (2008) [17 MeInfoText: Associated Gene Methylation and Cancer Information from Text Mining, Fang, Y.-C., Huang, H.-C.*, Juan, H.-F., BMC Bioinformatics 9, 22 (2008)


Research Activities of Individuals Research Activities on Interdisciplinary Research Cheng-Hung Chang (Institute of Physics, National Chiao Tung University; email: [email protected]) Center Scientist, 2007/2/1~2009/1/31

y research progress in this year can be divided into three disciplines: (I) biological motors, (II) spintronics, and (III) quantum chaos. The results are summarized as follows.

(I) Biological motors Most proteins have electric dipoles and net charges in the structure and their conformations are susceptible to the electric and magnetic perturbation. The shape of a cell may also amplify an electric field across its plasma membrane. Therefore, a membrane integral protein such as an ion channel, an ion pump, or a molecular motor, is especially amenable to electric perturbation. When an alternating electric field or a fluctuating electric field is employed to actuate a two-state protein oscillator, the dynamics of the conformational change of the protein can be synchronized with the applied field. Through this two-state protein oscillator, we construct a four-state catalytic wheel by coupling an energy transducer mechanism to the two-state protein oscillator [1]. Analysis shows that the catalytic wheel can extract energy from a disordered external energy source, be it electrical, mechanical, or chemical, and convert this stochastic energy source to a usable energy format. The catalytic wheel is tested with the experimental data on the electric field-stimulated cation pumping of Na, K-ATPase. A dipole ratchet model based on the electroconformational coupling concept will also be discussed and compared with the

Research Activities of Individuals -›› 144

ATP-dependent rotation of a rotary motor F1ATPase. Since the working principle of this model is simpler than that of F1-ATPase, it provides an easier way to realize a nanoscale rotary motor than artificially reconstructing a F1-ATPase.

(II) Spintronics In Ref. [2], we investigate the carrier-mediated exchange coupling between two ferromagnets, sandwiching an intermediate thin layer with Rashba interaction. The effective exchange coupling is obtained by integrating out the itinerant carriers. It turns out that the magnetic trends depend sensitively upon the topology of the Fermi surface. As the topology changes from "wedding cake" to "donut", the mediated exchange goes from the oscillatory RudermanKittel-Kasuya-Yosida to the non-collinear spiral interactions accordingly. It is rather surprising that the Fermi surface topology determines which type of magnetic interaction becomes dominant. Finally, we also discuss potential applications for carrier-mediated exchange coupling across the junction.

(III) Quantum chaos The correspondence principle in quantum mechanics states that in the semiclassical limit h → 0 classical mechanics emerges and governs quantum mechanical quantities for small de Broglie wavelength. One manifestation of this principle is that the Wignerfunctions of eigenfunctions converge weakly to invariant probability measures on

phase space, the so-called quantum limits (QLs). It is one of the big open problems in the field to classify the set of QLs, and it is in general not known which invariant measures can occur as QLs. For ergodic classical systems, the celebrated quantum ergodicity theorem states that almost all eigenfunctions have the ergodic Liouville measure as QL. If all eigenfunctions converge to the Liouville measure, it is called quantum unique ergodicity (QUE). Possible exception for QUE is strong scarring, i.e., QLs concentrated on periodic orbits and mixed classical systems, i.e., the phase space has several invariant components of positive measure. Less is known to what extent the quantum mechanical system respects the splitting of the classical system into invariant components. In Ref. [3], we introduce a class of model systems for which the set of QLs can be determined very precisely. This work provides a very rare example that a quantum ergodic map is not QUE.

machines, Nano 2, No. 5, 273–280 (2007). [2] Wen-Min Huang, Hsin-Hua Lai, ChengHung Chang, Hsiu-Hau Lin, Carriermediated exchange coupling and Fermi surface topology, International Journal of Modern Physics B, 22, Nos. 1 & 2 88–93 (2008). [3] Cheng-Hung Chang, Tyll Krueger, Roman Schubert, Serge Troubetzkoy, Quantisations of piecewise parabolic maps on the torus and their quantum limits, Communication in Mathematical Physics 282, 395–418 (2008).

References [1] Cheng-Hung Chang and Tian-Yow Tsong, Energy transduction in molecular

145 ‹‹- Research Activities of Individuals

Research Activities on Quantum Information Science Yueh-Nan Chen (Department of Physics, National Cheng-Kung University; email: [email protected]) Center scientist, 2006/10/13~2008/10/12

y research is mainly on the theory of quantum information science. There are four major results in the past year:

(II) Decoherence of a charge qubit embedded inside a suspended phonon cavity

(I) Proposal for observation of retardation effect between two quantum dots via current noise

We elucidate the theory of phonon-induced decoherence of a double dot charge qubit that is embedded inside a suspended semiconductor slab (Fig. 2). The influences of the lattice temperature, width of the slab, and positions of the dots on the decoherence are analyzed (Fig. 3). Numerical results indicate that the decoherence in the slab system is weaker than that in a bulk environment. In particular, the decoherence is markedly suppressed by the inhibition of the electron-phonon coupling. Such a system with low decoherence may be useful for manipulating the qubits..

We propose to observe the retardation effect between two quantum dots in a onedimensional waveguide. The effect of retardation is more pronounced comparing to that in free space. If the photons are to be reflected by a mirror at one of the ends, the interference role played by the reflecting photon is found to be destructive. With the combination of p-i-n junction, the retardation effect can be read out via current-noise spectrums (Fig. 1).

Fig.2 (a) Schematic view of a DQD embedded in a suspended semiconductor slab with a width of w. The surfaces of the slab are z= ±w/2, and the dots are located at z=0. (b) The top view shows that two identical dots are performed with the dot radii of a and interdot distance of d.

Fig. 1 (a) Schematic view of the two dots embedded in a p-i-n junction, such that the electron and hole can tunnel into QD 2. (b) Current-noise spectrums of the system with(black line)/without(green line) the consideration of retardation. The blue-dashed and red-dashed curves respectively represent the real parts of the memory functions.


An additional term from non-Markovian effect is obtained in the derivation of noise spectrum. As examples, two practical photonic reservoirs, photon vacuum with the inclusion of cut-off frequency and surface plasmons (Fig. 5), are given to show that the noise may become super-Poissonian due to this nonMarkovian effect. Utilizing the property of super-radiance is further suggested to enhance the noise value.

Fig. 3 (a) Quality factor Q as a function of tunneling coupling ∆ for slab and bulk systems (upper inset). The temperatures are T=20 mK (black solid line), 200 mK (red dashed line), and 400 mK (blue dotted line), respectively. A drastic enhancement of quality factor is found to be independent of temperature (arrow). (b) Dependence of the specific tunneling couplings ∆ for perfect quality factor on the width w. The corresponding period of time-dependent population is shown in the lower inset.

(III) Proposal for detection of nonMarkovian decay via current noise We propose to detect non-Markovian decay of an exciton qubit coupled to multimode bosonic reservoir via shot noise measurements. Non-equilibrium current noise is calculated for a quantum dot embedded inside a p-i-n junction (Fig. 4).

Fig.4 Schematic view of a QD p-i-n junction with its exciton coupled to a bosonic environment.

Fig. 5 Shot-noise spectra of QD excitons in front of a silver surface. The black, red, and blue lines represent the results of various dot-surface distances: d=0.1, 0.045, and 0.03 (in units of /2 = 1423Å), respectively. The inset shows the corresponding curves of the imaginary part of A(i ).

(IV) Entanglement detection via the condition of quantum correlation We develop a necessary condition of quantum correlation. It is utilized to construct a d-level bipartite Bell-type inequality which is strongly resistant to noise and requires only analyses of O(d) measurement outcomes compared to the previous result O(d2). Remarkably, a connection between the arbitrary highdimensional bipartite Bell-type inequality and entanglement witnesses is found. Through the necessary condition of quantum correlation, we propose that the witness operators to detect truly multipartite entanglement for a generalized GreenbergerHorne-Zeilinger (GHZ) state with two local measurement settings and a four-qubit singlet state with three settings. Moreover, we also propose a robust entanglement witness to detect a four-level tripartite GHZ state with only two local measurement settings.


References [1] Yueh-Nan Chen and Lukas Gilz, Appl. Phys. Lett., accepted (2008). [2] Y. Y. Liao, Y. N. Chen, W. C. Chou, and D. S. Chuu. Phys. Rev. B 77, 033303 (2008). [3] Y. N. Chen and G. Y. Chen, Phys. Rev. B 77, 035312 (2008). [4] C. M. Li, L. Y. Hsu, Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. A 76, 032313 (2007).


Research Activities on Particle Physics Phenomenology Kingman Cheung (Department of Physics, National Tsing Hua University; email: [email protected] Center Scientist, 2006/11/1~2008/10/31

joined the Center as a Center Scientist on November 2006. I am also the convener for the focus group on "Collider, Astroparticle and BSM". My research area is in particle physics phenomenology.

(I) Introduction The Large Hadron Collider should have started running when this report is published. It will be the place for the next big discovery. More than half of the resources in high energy community will be put into it. Together with other planned cosmology experiments, testing new ideas beyond the standard model (SM) will be the major activities in the next 10-20 years. My role is to link up theory and experiments. In past few years, I have accomplished a number of works on supersymmetry, Higgs physics, unparticles, and other new physics. In the following, I highlight a few topics that I feel very exciting.

(II) Higgs boson and supersymmetry The dominance of h ➝ a1a1 decay mode for the intermediate mass Higgs boson is highly motivated to solve the little hierarchy problem and to ease the tension with the precision data. However, the emergence of h ➝ ηη decay mode has undesirable effects on the golden search modes (h➝ γγ , bb) of the Higgs boson at the LHC. This will significantly worsen the chance of detecting an intermediate-mass Higgs boson at the LHC. In a Letter [1], we explicitly showed that the associated production of the Higgs boson with a W or Z boson can recover the loss of sensitivity in the golden modes. With the Higgs boson decaying into two pseudoscalar bosons, which further decay into 4 b jets, together with at least a charged lepton from the W or Z boson decay, a significant Higgs boson signal is observable at the LHC. We found that

the invariant mass spectrum of the 4 b-tagged jets can beautifully distinguish the Higgs signal peak from the continuum background. The result is very important to future search for the Higgs boson at the LHC. Since the ultimate goal of the LHC is hunt for the Higgs boson, which is responsible for electroweak symmetry breaking and mass generation, our work fully establishes the feasibility in searching for the intermediate-mass Higgs boson if h➝ηη dominates and solves the little hierarchy problem. In another work [7], we discuss a likely scenario at the LHC. What if only a light Higgs boson is discovered at the CERN LHC? Conventional wisdom tells us that the scattering of longitudinal weak gauge bosons would not grow strong at high energies. However this is generally not true. In some composite models or general two-Higgsdoublet models, the presence of a light Higgs boson does not guarantee complete unitarization of the WW scattering. After partial unitarization by the light Higgs boson, the WW scattering becomes strongly interacting until it hits one or more heavier Higgs bosons or other strong dynamics. We analyze how LHC experiments can reveal this interesting possibility of partially strong WW scattering. Little Higgs models are interesting alternatives to supersymmetry. A good example is the SU(3) simplest little Higgs model, which accommodates a light pseudoscalar boson η with quite different characteristics from those in other multiHiggs-doublet models. We study various phenomenological signatures of the η at the LHC in a work [8]. In particular, we calculate in details both production and decays in the Drell-Yan type channel qq¯ ➝ Z/Z' ➝ hη , and in the associated production with a t t¯ pair,


qq(qq¯ ) ➝ tt¯η. We emphasize the τ + τ - decay mode of the η boson when its mass is below the bb threshold. We show that tt¯η production is in fact large enough to give a sizable number of events while suppressing the backgrounds. We also comment on the direct gluon fusion process and the indirect decay from the heavy T quark (T➝ tη).

(III) Unparticle physics This has been an exciting topic in particle physics. We finished two important papers on this subject in 2007 [2,3]. One was published in Physical Review Letters and the other one in Physical Review. They received more than 200 citations in SPIRES database. The latter contains the formalism, derivations, and the results for important phenomenology of unparticle. The paper is well cited and useful to others. We continued to work on a few more interesting phenomena in unparticle stuff, and published three more papers on the subject in 2008. The subject is about the scale invariance or, in broader terminology, conformal invariance. Our existing particle theory is not conformal invariant, as the invariance is obviously broken by all the discrete masses of particles. Banks and Zaks in the 80s showed that a number of supersymmetric field theories contain a conformal window such that the theories can develop IR fixed points, where the scale is invariant. Recently, perceived by Georgi a scale invariant sector (coined unparticle) with a nontrivial infrared fixed point at a higher energy scale may actually describe the real world at high energy. So he visualized what kind of physics that such a sector can induce in high energy phenomenology. The unparticle with a scale dimension dU can be interpreted as a collection of dU invisible massless particles, which can be unveiled by measurements of various energy distributions in the processes Z➝ ff¯U and e-e+➝ —>γU at e-e+ colliders, as well as mono-jet production at hadron colliders. Our first two papers not only discovered the novel propagator effect of the unparticle but


also laid down the formalism for calculations and identified the important channels to observe unparticle effects at high energy colliders. The novel features, induced by scale invariance, include effective 4-fermion interactions and a nontrivial phase factor, which interferes with the SM amplitudes in an interesting manner The spectacular phase factor exp(–id U π ) associated with the propagator in s-channel can give rise to nontrivial behavior in a number of processes. In a work [4] with Li from Peking University, we worked out the decay of the standard model Higgs boson into a single photon and a vector unparticle through a oneloop process is studied. For an intermediate mass Higgs boson, this single photon plus unparticle mode can have a branching ratio comparable with the two-photon discovery mode. The emitted photon has a continuous energy spectrum encoding the nature of the recoil unparticle. It can be measured in precision studies of the Higgs boson after its discovery. In another work [5], we study the decay of the standard model Z boson into unparticle plus a single photon through a one-loop process. As in the anomaly type decay, only the axial-vector part of the Z coupling matching with the vector unparticle and/or the vector part of the Z coupling matching with the axial-vector unparticle can give a nonzero contribution to the decay. We show that the photon spectrum terminates at the end point in accord with Yang's theorem. Existing data on single photon production at LEP I is used to constrain the Photon-photon can occur in the standard model only via loop diagrams and is naturally suppressed. Unparticle can induce tree-level photon-photon scattering through the operator Fµν FµνOU for spin-0 unparticle or Fµα FανOµνU for spin-2 unparticle. Due to the peculiar CPconserving phase exp(–idUπ) associated with the time-like unparticle propagator for nonintegral scaling dimension dU, the interference effects of the s-channel amplitude with the tand u-channels ones on the total cross sections as well as the angular distributions are found to

be of some significance [6]. In addition, we show that the cross sections via unparticle exchange can be substantially larger than the standard model contribution.

(IV) Other topics I am also interested in some bound states that are recently discovered. The newly observed Z+ (4433) resonance by BELLE is believed to be a tetraquark bound state made up of (cu)(c¯d¯). We propose [10] the bottomed analog of this bound state, namely, by replacing one of the charm quarks by a bottom quark, thus forming Zbc0, ±,±±. One of the Zbc is doubly charged. The predicted mass of Zbc is around 7.6 GeV. This doubly-charged bound state can be detected by its decay into Bc±π ±. Similarly, we can also replace both charm quark and antiquark of the Z+ (4433) by bottom quark and antiquark, respectively, thus forming Zbb the bottomonium analog of Z+(4433). The predicted mass of Zbb is about 10.7 GeV.

[3] K. Cheung, W.-Y. Keung, and T.-C. Yuan, Phys. Rev. D76, 055003 (2007). [4] K. Cheung, C.S. Li and T.C. Yuan, Phys. Rev. D 77, 097701 (2008). [5] K. Cheung, T.W. Kephart, W.Y. Keung and T.C. Yuan, Phys. Lett. B 662, 436 (2008). [6] C.F. Chang, K. Cheung and T.C. Yuan, Phys. Lett. B664, 291 (2008). [7] K. Cheung, C.W. Chiang and T.C. Yuan, arXiv:0803.2661 [hep-ph]. [8] K. Cheung, J. Song, P. Tseng and Q.S. Yan, arXiv:0806.4411 [hep-ph]. [9] K. Cheung, X.H. Wu and Q.S. Yan, Phys. Rev. D 76, 116006 (2007). [10] K. Cheung, W.Y. Keung and T.C. Yuan, Phys. Rev. D 76, 117501 (2007).

References [1] K. Cheung, J. Song, and Q.-S. Yan, Phys. Rev. Lett. 99, 031801 (2007). [2] K. Cheung, W.-Y. Keung, and T.-C. Yuan, Phys. Rev. Lett. 99, 051803 (2007).


Research Activities on Quantum Information Science Chung-Hsien Chou (Department of Physics, National Cheng Kung University; email: [email protected]) Center Scientist, 2007/8/1~2009/7/31

n 2008 my research activity in NCTS has been focused on quantum information science. Most of the work was on quantum entanglement dynamics in relativistic motions and macroscopic quantum phenomena (MQP). In an earlier paper [1] we showed the derivation of an exact master equation for two coupled quantum harmonic oscillators interacting bilinearly with a common environment made up of n harmonic oscillators at an arbitrary temperature for a general spectral density function. This equation can be applied to the analysis of model problems in MQP involving two harmonic oscillators, either mechanical such as the superposition of two mirrors, or one of them of electromagnetic or superconducting flux origin, as in nanoelectromechanical (NEM) resonators or SQUID-resonator. For the dynamics of quantum entanglement between two qubits different environmental settings could lead to very different results. Most of the discussions on quantum entanglement dynamics are non-relativistic and with an implicit assumption that the background spacetime is globally Minkowski. Together with Dr. S.Y. Lin at NCTS and Prof. B.L. Hu from UMD we considered the quantum entanglement dynamics that was arising from nontrivial global structure of spacetime such as the existence of an event horizon, as in the spacetime of a black hole (Schwarzschild) or a uniformly accelerated detector (UAD) [2]. This is an important ingredient for the establishment of relativistic quantum information theory. In this work we study the dynamics of quantum entanglement between two Unruh-DeWitt (UD) detectors (atoms), which are point-like objects with internal degrees of freedom described by


harmonic oscillators, one stationary (Alice) and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in (3+1)D Minkowski space. These two detectors are set to be entangled initially, while the initial state of the field is the Minkowski vacuum. The covariant formalism can account for the fully relativistic effects. Our treatment is non-perturbative and with back-reaction automatically included in a selfconsistent way. We also address some of the key issues such as "sudden death" and entanglement revival, entanglement in different coordinates, and spatial separation between two detectors. Following this dimension of consideration, we are now studying the issue of decoherence and disentanglement in a dynamical background spacetime [3]. Another important issue is the demarcation between microscopic, mesoscopic and macroscopic. At the conceptual level we want to examine the validity of an implicit assumption made in many MQP investigations, namely, that the quantum mechanical behavior of a macroscopic object like the NEM or a C60 molecule, placed in interaction with an environment, behavior such as quantum decoherence, fluctuations and dissipation, entanglement and teleportation, can be captured by its centor-of-mass behavior. In an earlier paper [4] in collaboration with Prof. Yu and Prof. B.L. Hu, we took a small step towards treating the quantum properties of a mesoscopic or macroscopic object in a general environment by providing the technical base for such studies. Now we are pursuing further on the micro-to-macro transition.

References: [1] C.H. Chou, T. Yu, and B.L. Hu, Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment, Phys. Rev. E 77, 011112(2008). [2] S.Y. Lin, C.H. Chou, and B.L. Hu, Disentanglement of two harmonic oscillators in relativistic motion, arXiv:0803.3995[gr-qc], submitted to Phys. Rev. D. [3] C.H. Chou, S.Y. Lin, and B.L. Hu, in preparation.

[4] C.H. Chou, B.L. Hu, and T. Yu, Quantum Brownian motion of a macroscopic object in a general environment, Physica A 387,432(2008).


Research Activities on String Kazuyuki Furuuchi (email: [email protected]) Staff Scientist, 2007/8/1~2009/7/31

n this academic year, my research activity in NCTS was mainly focused on following three subjects in string theory.

(I) Description of thermodynamics of Yang-Mills theory on three dimensional sphere by effective matrix model of Polyakov loops, and black hole thermodynamics in anti-de Sitter space AdS-CFT correspondence is a conjectural equivalence between closed string theories in anti-de Sitter space and conformal field theories in lower dimension. The duality can be "explained" from extrapolation from openclosed string duality in perturbative string theory, though rigorous proof is difficult since it is beyond the region of validity of perturbative open or closed string theory. However, evidences found in the past ten years are enormous and it provides us a very strong tool to tackle issues in quantum gravity (gravity is contained in closed string theory). Thermodynamics in AdS-CFT correspondence is particularly interesting because one of the most intriguing puzzles about gravity is thermodynamical nature of black holes. In AdS(5)-CFT(4) correspondence (5 and 4 refer to space-time dimensionality), it has been argued that the cofinement-deconfinement transition in large N N=4 super Yang-Mills theory is a dual description of Hawking-Page transition, a transition from AdS geometry to AdS-black hole geometry. I have pointed out a relation to vortex condensation on the string worldsheet in my past research [1]. The thermodynamical phases of Yang-Mills theories on three dimensional sphere are governed by effective unitary matrix model of Polyakov loops. In ref. [2], I have constructed string field theory from the unitary matrix model using the techniques in old matrix


model, and provided a framework to describe the Hawking-Page transition as condensation of winding strings. As a continuation of the above series of works, in this academic year at NCTS I initiated construction of D-branes as solitons in string field theory. D-branes are regarded as solitons in closed string field theory and they played crucial roles in recent developments of string theory. But in order to really describe Dbranes as solitons, field theoretical framework for closed strings is necessary. However, closed string field theory has very complicated structure and partial success has been made in the past. My string field theory constructed from effective matrix model of Polyakov loops is a much simpler effective theory, and constructing D-branes in this model will help understanding above issue as well as uncovering roles of D-branes in black hole physics. I found D-brane field in my model is given by fermionization of string field [3]. This result is similar to what has been found in the Hermite matrix models, but the new feature here is that the analogue of string length in the Hermitian matrix model is winding number in the unitary model, but "negative length" in Hermitian model has more natural interpretation in unitary matrix model as winding number in opposite direction. This feature leads to doubled degrees of freedom of left and right movers in string field and Dbrane field in the case of unitary matrix model. From discussions with Prof. Fukuma at Kyoto University and Dr. Irie at NTU, I began to recognize that these D-branes may be useful for probing space-time geometry in the above AdS-CFT correspondence at finite temperature. I hope to clarify this issue in the near future.

(II) Space-time supersymmetry algebra in the model for multiple membranes M-theory is a hypothetical theory which is expected to provide unified description to five types of ten-dimensional superstring theory. However, only some parts of its structure in some specific limits are currently understood. One of the expected features of M-theory is that super-membrane is one of the fundamental building blocks of the theory. In the case of Dbranes which played crucial roles in the developments in non-perturbative studies of string theory in the last ten and some years, Lie algebra structure of multiple D-branes was a characteristic new feature. From this experience, we can expect that if we find characteristic algebraic structure of multiple membranes, our understanding of M-theory will make progress. From the end of 2006 towards the end of 2007, Bagger and Lambert constructed a model for multiple supermembranes which has a novel gauge symmetry based on Lie 3-algebra, a natural extension of Lie algebra (also Gustavsson 2007, 2008). After Mukhi and Papageorgakis showed a way to relate it to multiple D2-brane action in type IIA superstring theory, huge interests were attracted on this model. In ref. [4], together with Sheng-Yu Darren Shih at NTU and Tomohisa Takimi at NCTU, I studied supersymmetry algebra of the Bagger-Lambert Gustavsson model (BLG model). In particular, we tried to construct space-time supersymmetry algebra, which does not manifestly present in the original model. However, we almost fully obtained space-time superalgebra. This result suggests a relation to some space-time covariant formulation, and this is an interesting direction for future investigation. Central charges of the supersymmetry algebra provide important information of BPS objects in the BLG model. We found that in order to construct M5-brane charges, Lie 3-algebra structure is essential. This result provides an explanation for why in the matrix model of M-theory, a model based on Lie algebra and conjectured to describe Mtheory, M5-brane charge was absent, and

shows an advantage of the BLG model. We are currently working on how the BLG model from can be obtained from covariant M5-brane action. This is the direction suggested by the result of ref. [4], as I mentioned above. This is important in order to understand the relation between the new model of multiple membranes and currently understood part of M-theory. Discussions with Prof. Pei-Ming Ho at NTU who is one of the leading researchers in this field were particularly helpful in this project.

(III) Cubic open string field theory in linear dilaton backgrounds Recently, there was a rapid progress in construction of classical solutions in cubic open string field theory. Cubic open string field theory in linear dilaton backgrounds is interesting because 1. light-like linear dilaton backgrounds is one of rare time-dependent exact string backgrounds. 2. The gradient of dilaton backgrounds induces novel type of classical solutions. With Syoji Zeze who was a postdoc at NTU and moved to Yokote Seiryo high school, we constructed cubic open string field theory in linear dilaton backgrounds, in particular, explicit form of three-stringinteraction vertex. From this result we naturally obtained the string field theoretical version of the field re-definitions used in the paper of Pei-Ming Ho and Sheng-Yu Darren Shih, who were also our discussion partners. We also try to construct new solutions in two dimensional string theory, where comparison with another strong method, matrix model, is possible. Progress of this project has been slowed down a little since Dr. Zeze became busy for moving to his new job place, and during that period my main research focus was shifted to the model of multiple membranes mentioned above. However, we hoped to complete this project after Dr. Zeze settles down.


References [1] Kazuyuki Furuuchi, "From free fields to AdS: Thermal case," Phys. Rev. D72, 066009 (2005); Kazuyuki Furuuchi, "Confined phase in the real time formalism and the fate of the world behind the horizon," Phys. Rev. D73, 046004 (2006); Kazuyui Furuuchi, "Lectures on AdS-CFT at weak 't Hooft coupling at finite temperature," arXiv:hep-th/0608181. [2] Kazuyuki Furuuchi, "Matrix model for Polyakov loops, string field theory in the temporal gauge, and winding string condensation in anti-de Sitter space," arXiv:hep-th/0608108. [3] Kazuyuki Furuuchi, "Matrix Model For Polyakov Loops, String Field Theory In The Temporal Gauge, Winding String Condensation In Anti-de Sitter Space And Field Theory Of D-branes," Modern


Physics Letters A Special Issue °V 2007 International Symposium on Cosmology and Particle Astrophysics Vol. 23, Nos. 17-20 (2008) pp.1565-1576. [4] Kazuyuki Furuuchi, Sheng-Yu Darren Shih, Tomohisa Takimi, "M-Theory Superalgebra From Multiple Membranes," to appear in JHEP.

Research Activities on Cosmic Acceleration and Dark Energy Je-An Gu (National Taiwan University Leung Center for Cosmology and Particle Astrophysics; email:[email protected]) Assistant research scholar, 2006/8/1~2008/8/31

y research is focused on the cosmic acceleration and dark energy: understanding its behavior and its origin from both the phenomenological and the theoretical point of view. The existence of the cosmic acceleration at the present epoch was first discovered in 1998 via type Ia supernova (SN Ia) observations, and was further reinforced recently by updated SN Ia data, WMAP measurement of cosmic microwave background (CMB) and the observations of large-scale structures. Many explanations for this mysterious phenomenon invoke some exotic energy source, as generally called "dark energy", which provides significant negative pressure and repulsive gravity to drive the cosmic expansion to accelerate. The current status is: there exist many dark energy models that the current observations cannot distinguish. Accordingly, from the phenomenological point of view the most urgent issue at the present stage is to extract dark energy information as much and as efficiently as possible from the current and the near future observations and experiments. In addition, from the theoretical point of view the naturalness and the link with the fundamental physics have been two important key issues since the discovery of the cosmic acceleration.

(I) Phenomenological Approach For the phenomenological study I am interested in extracting physical information about dark energy from observations, in particular, in a model-independent manner. Observations which can map out the expansion history of the universe, such as the distance measurement of type Ia supernovae, are crucial probes of dark energy. With regard to the physical information about dark energy,

it is essential to answer two basic questions: (1) whether dark energy is played by a cosmological constant and (2) whether the dark energy equation of state changes with time. In the process of obtaining the dark energy information from data, a suitable parametrization is needed, especially when one requires the model independence. It was found that the information one obtains from data could be affected by the choice of the parametrization. Furthermore, the current model-independent parametrizations may be intrinsically incompatible with (thereby disfavoring) a significant part of models. (I-1) In the work in collaboration with Mr. Yu-Hsun Lo (master student) and Dr. Qi-Shu Yan at the National Tsing-Hua University (NTHU) we proposed a new parametrization (based on the Fourier series expansion) that is particularly reasonable and controllable [1]. We have tested the efficiency of distinguishing dark energy models with the use of this parametrization for analyzing the current and the future supernova data. As a result, we found it as good as the so-called "standard parametrization" proposed by Linder even for the simplest version of our parametrization. In addition to the goodness in distinguishing models, we emphasize that it is systematical and controllable to extend our parametrization with more parameters for accommodating more detailed and more complicated behavior (that is necessary particularly when the data become much richer and much more accurate in the future). (I-2) In the work in collaboration with Chien-Wen Chen (Ph.D. student) at the National Taiwan University (NTU) and Professor Pisin Chen at the NTU and the Stanford Linear Accelerator Center (SLAC) we proposed a new approach to constraining the quintessence models [2], which can also be


extended to other dark energy models. In this approach firstly we reconstruct the quintessence potential with observational data via the model-independent parametrization proposed by Linder. We then compare the reconstructed potential with those considered in quintessence models for the purpose of identifying the potential and constraining quintessence models. To facilitate this comparison, we propose that for each category of quintessence models one introduce a distinct characteristic that bridges observational results and the models under consideration. As a demonstration of the effectiveness of this approach, we examine the power-law potential and the exponential potential. As a result, we conclude that at the 68% confidence level both are ruled out, but at the 95% confidence level the power-law potential with a negative power between -2 and 0 can fit the data, while the exponential potential remains disfavored. For the future works, the modelindependent reconstruction of other dark energy models (in addition to quintessence) from data is worth of investigation. In addition to the model-independent parametrizations, I plan to explore the model-oriented parametrizations, i.e., which are optimized for or motivated by certain categories of models, such as quintessence, phantom, modified gravity, etc. For both two kinds of parametrizations, their stability and their compatibility with a variety of models are going to be investigated.

(II-1) For the naturalness I explored a mechanism to control the cosmological constant through a scalar field non-minimally coupled to gravity [3]. By utilizing nonminimal phantom or quintessence, the cosmological constant can be automatically driven to a value (which, in particular, can be positive in the phantom case) on the scale of the mass parameter in the phantom/quintessence potential V( ). The reduction of a large cosmological constant involves the weakening of gravity that therefore may be much stronger initially. I found the cases where originally gravity is on the TeV scale so that the hierarchy between gravity and three gauge interactions in the standard model of particle physics is bridged at the beginning. Although the cosmological constant can be automatically tuned or largely reduced under this mechanism, explaining the smallness of the observation-suggested cosmological constant energy density is still a difficult mission yet to be completed.

For the theoretical study, in the past 8 years I have been working on many different possible explanations of the cosmic acceleration, involving a variety of scenarios including cosmological constant, quintessence, phantom, extra dimensions, modified gravity and inhomogeneities of the universe. Recently, I focused on quintessence and phantom.

(II-2) For both the naturalness and the link with the fundamental physics I investigated rapidly oscillating quintessence [4,5]. There has been the suggestion that a rapidly oscillating scalar field can play the role of dark energy. The case of a power-law potential is particularly intriguing, where the equation of state w oq of dark energy is a constant determined simply by the power n in the potential through w oq = (n-2)/(n+2). In the recent work I focused on the power-law potential, and investigate the condition for oscillation and the constraints from the current observations. For this oscillating quintessence scenario I found a specific model with much less fine tuning, where all of the dimensionful parameters and the period of oscillation are on the same scale as the energy density of the present universe. This natural model provides a working example that largely increases the feasibility of oscillating quintessence.

Along the direction of addressing the two key issues mentioned earlier, the naturalness and the link with the fundamental physics, I investigated two models: (1) non-minimally coupled phantom and quintessence; (2) oscillating quintessence.

For the future works, in addition to the theoretical studies oriented towards the two key issues mentioned above, I also plan to launch the investigations relevant to my current and future phenomenological works mentioned earlier, such as the establishment of

(II) Theoretical Approach


the model-oriented parametrizations and the test of the compatibility of parametrizations with models.

[5] Je-An Gu, "Can field excitations play the role of dark energy?" Mod. Phys. Lett. A 23, 1384 (2008).

References [1] Je-An Gu, Yu-Hsun Lo and Qi-Shu Yan, in preparation. [2] Je-An Gu, Chien-Wen Chen and Pisin Chen, "A New Approach to Constraining Quintessence Models by Observations," submitted for publication, arXiv: 0803.4504 [astro-ph]. [3] Je-An Gu, "Automatic Control over the Cosmological Constant through Nonminimal Phantom and Quintessence," submitted for publication, arXiv: 0801.4737 [hep-th]. [4] Je-An Gu, "Oscillating Quintessence," submitted for publication, arXiv: 0711.3606 [astro-ph].


Activities report on String Takayuki Hirayama (email: [email protected], [email protected]) Postdoctoral researcher, 2007/9/1~2009/8/31

became a member of NCTS on September 2007 and my activities since them are summarized into two topics. One is the application of so-called AdS/CFT into QCD ( Quantum Chromo Dynamics ) and the other is a black hole stability in a quantum level. I published one paper for each topic, [1] and [2]. The AdS/CFT is a conjecture in string theory which claims the equivalence between a string theory or supergravity on a curved space and a quantum field theory without gravity. The example which have been studied intensively is the duality between Type IIB string theory in a space of 5 dimensional Antide Sitter space times 5 dimensional sphere and the four dimensional N=4 supersymmetric Yang-Mills theory. This duality is a weakstrong duality in a sense that a weak string coupling region of Type IIB string theory is dual to a strong gauge coupling region of Yang-Mills theory. Therefore this AdS/CFT correspondence offers a quite powerful tool of computing a strongly coupled gauge theory from a weakly coupled gravity theory. QCD ( Quantum Chromo Dynamics ) is a gauge theory which describes the strong force in nature. The mesons and baryons are composites made of quarks which are bound by this strong force. Because of strong gauge coupling of QCD, it is quite difficult and challenging to compute the masses and interactions of mesons and baryons. I have challenged to compute the lightest mass state in QCD which is called the pion by applying the AdS/CFT correspondence into QCD. The dual description of QCD in terms of gravity is based on so-called D-branes in string theory.In [1] I and my collaborators succeeded to realize the observed value of pion mass by introducing another D-branes in the model. We showed that the pion mass is generated from the contribution of worldsheet instanton in


string theory. We alsocomputed the value of chiral condensate and showed the relation between the quark mass and the value of chiral condensate satisfies the Gell-Mann-OakesRenner relation. Now I continue working on this direction to compute the quark mass dependenceof mesons and baryons which is important when we study hadrons which contain s-quark. Another work on the black hole stability was carried out in [2]. Einstein gravity predicts black holes and the black hole physics is important in classical and quantum gravity. Especially the black hole thermodynamics has provided many implications of quantum properties of gravity. Gross, Perry and Yaffe showed that there is a negative mode around the Schwarzschild black holes which induces a decay process of hot flat space into nucleation of black holes. And there is a general expectation that the existence of negative mode and the instability of black hole as a thermodynamics ( the negative heat capacity in the case of Schwarzschild black hole ) are equal. In fact if we introduce a negative cosmological constant and a Schwarzschild black hole starts showing the thermodynamic stability, the negative mode disappears. String theory contains gravity and is a perturbatically well defined quantum theory. From studying the low energy effective theory of string theory, the low energy effective theory has additional higher dimensional terms in addition to Einstein gravity. Then there is a natural question that whether the equivalence between the existence of negative mode and the thermodynamic instability holds even there are higher dimensional correction terms expected from string theory. I studied this problem in [2] and found an unexpected result. For simplicity, I added the so-called GaussBonnet term into Einstein theory which is the lowest dimensional term among the

corrections and studied negative mode(s) around the Schwarzschild type black hole. When the black hole size is small enough so that the Gauss-Bonnet term becomes relevant, I found the equivalence no longer holds. This is quite unexpected since this equivalence is shown to be satisfied in many different black holes in Einstein gravity with matter and gauge fields, although there is no proof. At this moment I have not had physical understanding of my results.Therefore I have continued working on this project and expect more properties of quantum gravity can be revealed through this project.

References [1] Koji Hashimoto, Takayuki Hirayama, Feng-Li Lin, Ho-Ung Yee, Quark Mass Deformation of Holographic Massless QCD, published in JHEP 0807:089, 2008. [2] Takayuki Hirayama, Negative modes of Schwarzschild black hole in EinsteinGauss-Bonnet Theory, submitted to Classical and Quantum Gravity.


Research Activities on Condensed Matter Physics Wen-Hsuan Kuan (Department of Science, Taipei Municipal University of Education; email: [email protected]) Postdoctoral researcher, 2006/2/1~2008/7/31

y works in 2008 were briefly summarized as follows:

(I) Ground state properties and collective excitations of a dipolar Bose-Einstein condensate (BEC) Recently attained BEC gas of highly magnetic chromium atoms shows a signature of dipolar interactions. This opens a door for investigations on the dynamics of cold atoms in strong electric field under which the long range dipole-dipole interaction may have profound effect. Moreover, it provides a better understanding on the formation of the BEC molecules and the mechanism in BEC-BCS phase transition. Yi and You 1 first introduced a pseudopotential approach for describing slowly moving particles interacting via shortrange contact potential and the long-range dipolar force. However, their approach based on first Born approximation (FBA) that is valid only in the low energy scattering regime. The weak interaction assumption breaks down near scattering resonances. Therefore, it is crucial to develop a full many-body theory for dipole beyond FBA. In the recent work of Wang 2 , the first effective many-body theory that is capable to describe bosonic dipolar condensates even near the shape resonance (SR) or in the strongly interacting regime has been derived. Using the scattering matrix elements calculated by Deb et.al., the dipolar effect near SR is found to be significantly renormalized so that the system becomes more stable than what is predicted using simple FBA. Moreover, the elementary excitation of the 2D condensate behaves as q in the long wavelength limit, showing the same low energy physics as 2D charge bosons with Coulomb interactions.


Together with professor Daw-Wei Wang, we have derived the effective Hamiltonian beyond FBA in 3D, and the ground state energy has been calculated by using the Gaussian type trial wave function. However, it is inadequate to do so while the condensate profile is highly anisotropic. To remedy the flaw, we solved the dipolar Gross-Pitaevskii equation in a fully numerical manner. Also, we directly solved the many-body Hamiltonian. We used the Monte Carlo integration method in dealing with a many-dimensional calculation that provided the results all within great accuracy. Eventually, the optimal set of parameters of trial wave functions would be determined via the variational method in the sort of the lowest energy solution. The program is in progress. Based on our work, the further calculation in collective excitations can provide a comparison with ab initio calculations and the significance of dipolar effect can be quantitatively confirmed.

(II) Landau-level mixing effect on rotating BECs with attractive interactions in anharmonic trapping potentials Problems of rotating BECs have attracted much attention in the past years. In the rotating frame at frequency , BECs feel the Coriolis force which is identical to the Lorentz force of a charged particle with mass M in a magnetic field B = 2M . The analogy between the motion of charged particles in a magnetic field and neutral atoms in a rotating frame can reveal some interesting solid state phenomena such as vortex lattice, quantum Hall liquid and Wigner crystal in rotating BECs. Repulsive rotating BECs in a harmonic trapping potential can form a singly quantized vortex above a certain critical rotational frequency. When rotation frequency is close to

the harmonic trapping frequency, rotating BECs condense into the lowest Landau level (LLL) and form a vortex lattice. The centrifugal force cancels the trapping force, and BECs fall apart if rotational frequency is equal to the harmonic trapping frequency. It is interesting to know whether vortices can also exist for attractive BECs even attractive BECs having different physical phenomena compared with repulsive BECs. Attractive BECs are only stable for a sufficiently small number of particles or very weak interactions, but mutual interactions can be reduced by the Coriolis force for rotating atoms. In a harmonic trapping potential, instead of existing vortices, the energetically favored state of attractive rotating BECs is the center-of-mass (CM) motion which absorbs all the angular momentum of rotation.3 On the hand, vortex and CM states are attainable via an anharmonic term in the trapping potential to eliminate instability. Ground state properties of attractive rotating BECs have been studied perturbatively under the LLL approximations.4 To study systems with any arbitrary interaction strength and anharmonic trapping potential, an emergent theory beyond the perturbative approach is needed. Together with professor Szu-Cheng Cheng, in this work we calculated the energy functional of Gross-Pitaevskii equation by proposing variational wave functions of vortex and CM states within Landau-level mixing effects. We have proved that ground-state energies, without Landaulevel mixing, of vortex and CM states are consistent with the many-body perturbation theory. We also found that, in fact, the lowest energy of vortex or CM state should be the state including the effect of Landau-level mixing. The effect of Landau-level mixing is not negligible even under conditions of weak interactions and small anharmonic trapping potentials. Vortex and CM states, whose ground-state energies are lowered, are stabilized by the effect of Landau-level mixing.

Fig.1 Caption: The Phase diagram of a rotating condensate in a quadratic-plus-quartic potential in Ω/ 0– plane for =0.05. In extremely-weak interaction and highly-rotating speed regime, vortex state of large number of vortices is generated to lower the energy of the system. As the attractive interaction is enhanced to balance the centrifugal force and the anharmonic trapping force, the condensate energetically favors the center-of-mass motion. Before the collapse of the condensate, off-center vortex state can exist in the grey region due to Landau-level mixing effect.

(III) Generation of dc spin currents in narrow channel with Rashba and Dresselhaus spin-orbit interactions The success of dc front-gate control for the measurement of Rashba coupling strength inspired proposals for spin current generation by nonmagnetic means. These proposals include adiabatic quantum pumping in a quantum dot with static SOI interfaced with a time-dependent barrier and a spatially separated Rashba SOI region, and an ac-biased Rashba-type two-dimensional (2D) disorder system or quantum channel.5 It is known that the translational invariance is broken in the channel direction due to a spatially localized time-dependent potential, thus allowing us to explore coherent resonant inelastic scattering and time-modulated quasi-bound state features. Together with professor Chi-Shung Tang, we consider a narrow channel formed in a high-mobility electronic quantum well by applying negative bias on the front split gates. When a finger gate is deposited above the split gate separated by an insulating layer, a local time varying Rashba coupling parameter


(r,t)can be induced by ac-biasing the finger gate. We explored how the interplay among the static Rashba, the static Dresselhaus, and the dynamical Rashba SOI effects influences the efficiency of spin current generation in the absence of source-drain bias. The considered dynamical system for spin pumping is depicted in Fig. 2. The spin current generating features have been demonstrated and illustrated in detail. In Fig. 3, we demonstrate how the Dresselhaus spin-orbit coupling strength influences the dc spin current generated by the ac-biased front gate. Fig. 4 shows the spin-resolved transmission with dynamical Rashba coefficient. It has been found that the Dresselhaus spin-orbit coupling intends to suppress the efficiency of spin current generation in the low kinetic energy regime, while the Dresselhaus effect can enhance the pumped spin current in the high kinetic energy regime. 6 Unlike the parametric quantum pumping, in which two pumping potentials with a phase difference is needed. Our proposed spin current generating device is achievable using a single ac-biased gate, and should be achievable within recent fabrication capability.

Fig.3 Caption: (a): Spin-resolved current transmission TRL(solid red) and TRL(dashed blue) as a function of electron energy in units of driving frequency. (b): Generated dc spin current for the cases of 0= 0.0$ (dotted red), 0.02 (dashed green), and 0.04 (solid blue). L/L*=30, 0=0.13, 1=0.05, and \omega = 0.05∆ .

Fig.2 (sys.eps) Caption: Schematic illustration of the quantum wire with Rashba and Dresselhaus spin-orb interaction influenced by an ac-biased finger gate (with length L) across the wire.

Fig.4 Caption: (a): Spin-resolved current transmission TRL (solid red) and TRL (dashed blue) as a function of electron energy in units of driving frequency. (b): Generated dc spin current for the cases of =0.03 (dotted red), 0.04 (dashed green), and 0.05 (solid blue). L/L*=50, 0=0.13, 0=0.03, and \omega = 0.05∆ .


References [1] S. Yi and L. You, Phys. Rev. A 61, 041604 (2000); ibid. 63, 053607 (2001). [2] Daw-Wei Wang, arxiv:cond-mat/ 07043868 (2007). [3] N. K. Wilkin, J. M. F. Gunn, and R. A. Smith, Phys. Rev. Lett. 80, 2265 (1998). B. Mottelson, Phys. Rev. Lett. 83, 2695 (1999). [4] G. M. Kavoulakis, A. D. Jackson, and G. Baym, Phys. Rev. A 70, 043603 (2004). A. Collin, E. Lundh and K.-A. Suominen, Phys. Rev. A 71, 023613 (2005).

[5] L. Y. Wang, C. S. Tang, and C. S. Chu, Phys. Rev. B 73, 085304 (2006). [6] C. S. Tang, W. H. Kuan, W. Xu, and Y. C. Chang (accepted by JVST B 2008).


Reseach Activities on Lattice Gauge Theory in Physics of the Large Hadron Collider C.-J. David Lin (Institute of Physics, National Chiao-Tung University; email: [email protected]) Center Scientist, 2007/2/1~2009/1/31

ntroduction From August 2007 to August 2008, I started projects in physics related to the Large Hadron Collider using large-scale numerical simulations in Lattice Gauge Theory. This is reflected in two main research avenues that I am pursuing. First, I am studying the scenario of electroweak symmetry breaking via a strongly coupled gauge theory at TeV scale. Second, I am performing calculations for decay amplitude of baryons containing a b quark, which is the main subject of the LHC-b experimental project.

Hardware The start-up equipment fund for my position was granted in the summer of 2007, from the National Science Council and Faculty of Sience, National Chiao-Tung University. From August 2007 to December 2007, I played the main role in the purchase of a PC cluster using this start-up fund. The cluster was delivered between January and April 2008. Now it contains twenty-six computing nodes. Each node has two quad-code CPUs and sixteen gigabites of memory (with error checking). Twenty-two of these nodes are connected via a Double-Data-Rate (up to 20 gigabits per second) infiniband switch. The other four are on a gigabit network. In addition to the computing nodes, we have a six-terabite disc array for storage.

Physics of the b-baryon A b-baryon is composed of three valence quarks, namely, a b-quark and two light quarks. The rare decay channels in which a non-stranged b-baryon decays into a stranged baryon plus a photon or a lepton pair are sensitive to new physics effects involving the mixing of quarks via right-handed coupling


structure that is absent in the Standard Model. This structure cannot be probed by existing experiments performed with the B mesons which do not carry spin. With William Detmold and Matthew Wingate, I have set up a programme to pin down the relevant matrix elements in the above decay channel as our final goal. In our programme, we use the dynamical gauge configurations generated and kindly lent to us by the RBC Collaboration. The lattice size is 24-cube times 64, with lattice spacing around 0.1 fm. The 2+1 flavours of dynamical quarks in these RBC configurations are domain wall fermions. We also use the same fermions for our valence light quarks. For the heavy quark, we use the static approximation where the heavy-quark mass is infinite. The most time-consuming step in this programme is to generate light-quark propagators. We have finished two thirds of this task for our initial investigation after running the program on my PC cluster and other computing resources in the USA for five months. In lattice numerical simulations involving static heavy quarks, it is often important to study the choice of the quark-level interpolating operators for mesons and baryons. This is because the statistical noise from the Monte-Carlo simulation can become significant in this setting. To this end, we have investigated the two-point functions of these hadrons. In Fig. 1, two choices of parameters in the baryon interpolating operator are presented. Here we are plotting the logarithm of the ratio of the correlators at the nearest two euclidean lattice time slices as a function of time. A plateau in such a plot signals a baryon state in the simulation, and the value of this plateau is the baryon mass. From Fig. 1, it is clear that the parameters in the left panel are

much better than those in the right panel.

Once the spectrum is calculatd, we will proceed to the calculations of various relevant matrix elements.

Walking Technicolour

Fig. 1

As the first step towards the calculation of rare decay matrix elements of b-baryons, we have studied the spectrum of these baryons. In particular, we are investigating the light-quark mass dependence of the spectrum. There have been very few lattice calculations for the bbaryon spectrum, and the parameters (quark mass, lattice volume, etc.) in our work are the closest to the physical values. Fig. 2 presents the light-quark mass dependence of the mass difference between the Lambda-b baryon and the B meson. One can see some hint that there may be some non-linear dependence here, as predicted by Chiral Perturbation Theory. This was never observed before in heavy baryon systems, and we are currently generating more data to perform a detailed study. It will be published in the near future in Ref. [1].

Walking technicolour is one of the candidates that generate the electroweak symmetry breaking at TeV scale without the need for the Higgs particles. It is a stronglycoupled gauge theory, hence lattice gauge theory can play an important role in this research avenue. In the walking-technicolour scenario, the coupling constant in the gauge theory increases over a range of scale when the energy is decreased, then it becomes "frozen". At the very low energy regime, it starts increasing again, such that conformal symmetry and chiral symmetry are broken dynamically. The system then develops an energy gap which generates the spectrum. The reason why such a scenario is required is due to the need to dynamically suppress the flavour-changing neutral currents (FCNC) in physics beyond the Standard Model. A walking theory is likely to produce large anomalous dimensions for the operators that generate the Standard Model fermion masses. This can then lift the scale at which flavour emerges, hence suppress the FCNC. It is not easy even just to find a theory which has the "walking" feature and dynamical symmetry breaking at low energy. Exploratory result using the step-scaling method was reported by Appelquist and collaborators recently [2]. These authors calculated the coupling constant in the so-called Schroedinger functional scheme for QCD-like theories with large numbers of flavours. They discovered that the coupling constant would stop running for a


range of scale in some of these theories. However, this statement has to be checked in other schemes. At the moment, I have formed a collaboration with physicists in Professor Tetsuya Onogi's group at the Yukawa Institute at the University of Kyoto. We are studying the scale dependence of the coupling constant in these theories in the Creutz-ratio scheme. We fix the scheme by keeping constant the ratio between the Wilson-loop size and the lattice size, as indicated in Fig. 3. This specifies the scheme. We then perform calculations at various lattice sizes and extrapolate to the continuum limit at each step. The lattice size is the renormalisation scale in this procedure. Since this is a new scheme, we have performed exploratory numerical study of the coupling constant in the quenched prroximation for QCD. Our numerical data fit the two-loop running formula well at high energy [3,4], as shown in Fig. 4

Fig. 3

Fig. 4


At the moment, we are preparing the dynamical fermion simulations. In the future, we will also try to compute the running of the condensate in these theories. This is the most crucial point in hunting for a walking technicolour theory.

Reference [1] W. Detmold, C.-J.D. Lin and M. Wingate, "Lattice calculation of b-baryon spectrum with domain-wall light quarks", in preparation. [2] T. Appelquist, G. Fleming and E. Neil, "Lattice study of the conformal window in QCD-like theories", Phys. Rev. Lett. 100:171607, 2008. [3] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi and T. Yamazaki, arXiv:0808.2875 (Proceedings for Lattice 2008, to be published in Proceedings of Science). [4] E. Bilgici, A. Flachi, E. Itou, M. Kurachi, C.-J.D. Lin, H. Matsufuru, H. Ohki, T. Onogi and T. Yamazaki, "A new method of calculating the running coupling constant", in preparation.

Research Activities on Spintronics Hsiu-Hau Lin (Department of Physics, National Tsing Hua University; email: [email protected]) Center Scientist, 2006/2/1~2010/1/31

n the past year (2007-2008), I have continued my research on spintronics (S) and also low dimensional correlated systems (L), leading to the publications listed below. Let me briefly summarize our research results here and leave detail explanations for key findings in later paragraphs. On the spintronics part, we applied the developed self-consistent Green's function approach to nanoscale junctions and find the carrier-mediated exchange coupling strongly depends on the topology of the Fermi surface topology [S2,S4]. We also collaborate with experimentalists to see whether the theoretical predictions can be verified. In p-type Si film implanted with B and Mn ions, the theoretical predictions are in qualitative agreement with the experimental data [S3]. Furthermore, in a recent collaboration, we were able to achieve quantitative explanation of the magnetization curve in amorphous Si film doped with Cr [S1]. It is rather remarkable that the quantitative agreement between the theory and the experiment can be achieved by only one fitting parameter! [S1] Jia-Hsien Yao, Hsiu-Hau Lin and TsungShune Chin, Room temperature ferromagnetism in Cr-doped hydrogenated amorphous Si films. Appl. Phys. Lett. 92, 242501(2008). [S2] Wen-Min Hunag, Hsin-Hua Lai, ChengHung Chang and Hsiu-Hau Lin. Carriermediated exchange coupling and Fermi surface topology (invited article). Int. J. Mod. Phys. B 22, 88 (2008). [S3] Hung-Ta Lin, W.-J. Huang, S.-H. Wang, Hsiu-Hau Lin and Tsung-Shune Chin. pSi(100) by sequential ion-implantation of B and Mn. J. Phys.: Condens. Matter 20, 095004 (2008). [S4] Wen-Min Huang, Cheng-Hung Chang and Hsiu-Hau Lin. Non-collinear magnetic junction mediated by Rashba interaction. J. Mag. Mag. Mat. 310, e759 (2007).

On the low-dimensional correlated system side, we tried to address various physical properties in low dimensional systems including the charge-density wave formation [L3], conductance anomaly in carbon nanotubes [L4] and flat-band freeomagnetism in armchair graphene nanoribbon [L5]. One of the most striking feature we tried to investigate is symmetry restoration under renormalization group transformation. We devise an elegant transformation to map the metallic zigzag carbon nanotube to a non-conventional two-leg ladder (without inter-leg hopping) and found an approximate SO(6) symmetry in the neutral sector [L2]. Pursuing the same direction, we combine the techniques of the perturbative renormalization group and the nonperturbative bosonization to obtain global phase diagram for zigzag carbon nanotube [L1]. As the interaction strength decreases into the weak-coupling regime, symmetry restoration emerges giving rise to various nontrivial binding mechanism and also excitation degeneracy, which may help us to understand how non-conventional pairing arises in strongly correlated systems in low dimensions. [L1] J. E. Bunder and Hsiu-Hau Lin. Phase diagram of the metallic zigzag carbon nanotube. Phys. Rev. B 78, 035401 (2008). [L2] J. E. Bunder and Hsiu-Hau Lin. Dynamical Symmetry Enlargement in Metallic Carbon Nanotubes. Phys. Rev. B 75, 075418 (2007). [L3] Chao-Hung Du, Chung-Yu Lo, Hsiu-Hau Lin, Shih-Lin Chang, Nonlinearity and dynamic phase transition of chargedensity-wave lattice. J. Appl. Phys. 101, 104915 (2007). [L4] Po-Yao Chang, Wen-Min Huang and Hsiu-Hau Lin. Impurity induced conductance anomaly in zigzag carbon nanotube. accepted for publication in J. Phys.: Conf. Series (2008).


[L5] Yen-Chen Lee and Hsiu-Hau Lin. Flatband ferromagnetism in armchair graphene nanoribbon. accepted for publication in J. Phys.: Conf. Series (2008).

Diluted Magnetic Semiconductors Carrier-mediated ferromagnetism, found in diluted magnetic semiconductors (DMS) such as III-V semiconductors doped with transition metals, opens up the possibility of electric manipulations of magnetic and optical properties because of the exchange coupling between the localized moments of the transition metal and the itinerant spins in the semiconducting bands. In recent years, experimental progress has stimulated intense theoretical investigations of DMS those mainly focus on estimates of the critical temperature. Although some experimental data is available little theoretical attention has been paid to spin dynamics, which is crucially important in understanding the spin coherence.

On the other hand, the situation simplifies quite a bit if the carriers are localized. Applying the percolation of magnetic polarons, one can calculate the magnetization curve versus temperature. The only fitting parameter is the ratio between the size of the magnetic polaron and the mean distance between the magnetic dopants. We tried to compare the theoretical predictions and the experimental measurements in amorphous diluted magnetic semiconductors. In hydrogenated amorphous Si flim doped with Cr, the measured magnetization curve agrees with the theoretical prediction – with just one fitting parameter for the whole temperature range.

Symmetry Restoration in Carbon Nanotubes

It is important to emphasize that the carriermediated ferromagnetism can be roughly divided into two categories depending on the carriers are itinerant or localized. For itinerant carriers, the mediated exchange coupling sensitively depends on the band structure and also the thermal fluctuations. Although the band structure can be computed by the firstprinciples methods, however, the supercell approach works poorly for predicting the correct magnetic behaviors. On the other hand, the model approach can address more subtle issues like spin-wave fluctuations. But, it is rather difficult to integrate these theoretical methods with realistic band structures (often very complicated). Therefore, quantitative agreement between theories and experiments remain a tough quest.


Carbon nanotubes are fascinating materials with remarkable mechanical and physical properties. Due to their low dimensionality, correlations and quantum fluctuations arising from electron-electron interactions cannot be ignored. It was beautifully demonstrated theoretically and later verified in experiments that the unscreened Coulomb interactions drive the armchair nanotube into a TomanagaLuttinger liquid phase with exotic spin-charge separation. On the other hand, if the Coulomb interactions are screened so that only shortranged interactions remain, various instabilities set in and the ground state phase diagram is rather rich. As a carbon nanotube has only a few conducting channels, it is not obvious how the long-ranged Coulomb interactions can be screened. One proposal for the reduction of long-ranged Coulomb interactions is a thick arrangement of nanotubes in either array or rope form. Alternatively, one can make use of improving nanoscale technology and place a

carbon nanotube close to a conducting plate. The induced image charges in the conducting plate will render the Coulomb interactions short-ranged. While most theoretical investigations concentrate on the armchair nanotube because of its simplicity, it is often assumed that the low-energy physics should be the same for metallic zigzag carbon nanotubes, since for both honeycomb lattices the low-energy physics originates from the Dirac cones in the band structure. We looked into this issue carefully and found that the effective lattice model of the zigzag nanotube differs from that of the armchair. Ignoring the interactions momentarily, by integrating out the gapped modes, the metallic zigzag nanotube is described by an effective two-chain system. Note that the interchain hopping is absent in this effective lattice model. As a consequence, the Fermi velocities remain degenerate when the nanotube is doped away from half filling. It is important to emphasize that the Fermi velocities in the armchair nanotube are equal to each other only at half filling and become different at finite doping. As we will explain later, the degeneracy of the Fermi velocities in the zigzag carbon nanotube is crucially important for symmetry restoration at finite doping. In addition to the subtle velocity degeneracy at finite doping, the differences between the zigzag and armchair nanotubes' effective lattice models become obvious when one tries to write the effective interactions. It turns out that, after integrating out the gapped modes, the effective interactions for the zigzag are far more complicated than those for the armchair.

We reanalyze the correlation effects in the

effective two-leg lattice model with the oneloop renormalization group (RG) and the nonperturbative bosonization techniques. Due to the spreading of the wave function, the effective interaction strength is reduced by a factor of 1/N, where N is the number of unit cells around the circumference. This reduction in the effective interaction strength is crucially important as it allows the weak-coupling RG analysis to be valid.

The one-loop RG flows determine the instabilities which may then be analyzed by non-perturbative bosonization (and refermionization) in order to identify gaps in different charge and spin sectors. From this, not only can the phase diagram be determined, but our numerical results also reveal symmetry restoration of low-energy excitations above the ground state. For a truly weak interaction strength U/t

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