Relaxation dynamics of a quantum Brownian particle in an ideal gas

TL;DR

This paper derives a quantum Fokker-Planck equation from the quantum linear Boltzmann equation, providing microscopic expressions for diffusion and relaxation in a quantum Brownian particle within an ideal gas.

Contribution

It presents a derivation of the quantum Fokker-Planck equation as a diffusive limit of the quantum linear Boltzmann equation, including physical justification and microscopic coefficients.

Findings

Derived quantum Fokker-Planck equation from Boltzmann equation

Provided microscopic expressions for diffusion and relaxation coefficients

Discussed approximations and their physical basis

Abstract

We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.