Non-Markovian Markovian Markovian Caldeira—Leggett ... - arXiv

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We obtain a non-Markovian quantum master equation directly from the ... master equation on the basis of which we work out the concept of non-equilibrium.
NonNon-Markovian Caldeira— Caldeira—Leggett quantum master equation A. O. Bolivar

Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, Minas Gerais, Brazil Abstract

We obtain a non-Markovian quantum master equation directly from the quantization of a non-Markovian Fokker—Planck equation describing the Brownian motion of a particle immersed in a generic environment (e.g. a nonthermal fluid). As far as the especial case of a heat bath comprising of quantum harmonic oscillators is concerned, we derive a non-Markovian Caldeira—Leggett master equation on the basis of which we work out the concept of non-equilibrium quantum thermal force exerted by the harmonic heat bath upon the Brownian motion of free particle. The classical limit (or dequantization process) of this sort of non-equilibrium quantum effect is scrutinized, as well.

I. INTRODUCTION

From the mathematical point of view, the dynamics of an isolated material point is deterministically described by the Schrödinger equation ;

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