Non-Markovian Caldeira--Leggett quantum master equation

TL;DR

This paper derives a non-Markovian quantum master equation from a non-Markovian Fokker-Planck equation, extending the Caldeira-Leggett model to non-equilibrium quantum environments and exploring quantum thermal forces.

Contribution

It introduces a non-Markovian quantum master equation for Brownian motion in non-thermal environments, generalizing existing models to non-equilibrium quantum systems.

Findings

Derived a non-Markovian Caldeira-Leggett master equation.

Introduced the concept of non-equilibrium quantum thermal force.

Analyzed the classical limit of the quantum effects.

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 non-thermal 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.