Quantum kinetics and thermalization in a particle bath model

TL;DR

This paper investigates the relaxation and thermalization dynamics of a particle interacting with a harmonic oscillator bath, comparing exact solutions with Markovian and non-Markovian quantum kinetic approximations to understand their validity.

Contribution

It provides an exact solution for the particle's distribution evolution and derives a non-Markovian quantum kinetic equation including off-shell effects, highlighting limitations of traditional Boltzmann approaches.

Findings

Non-Markovian dynamics capture off-shell effects and formation times.

Boltzmann approximation fails for wide resonances and threshold effects.

Exact solutions reveal differences in relaxation between bare particles and quasiparticles.

Abstract

We study the dynamics of relaxation and thermalization in an exactly solvable model of a particle interacting with a harmonic oscillator bath. Our goal is to understand the effects of non-Markovian processes on the relaxational dynamics and to compare the exact evolution of the distribution function with approximate Markovian and Non-Markovian quantum kinetics. There are two different cases that are studied in detail: i) a quasiparticle (resonance) when the renormalized frequency of the particle is above the frequency threshold of the bath and ii) a stable renormalized `particle' state below this threshold. The time evolution of the occupation number for the particle is evaluated exactly using different approaches that yield to complementary insights. The exact solution allows us to investigate the concept of the formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles and that of quasiparticles. We derive a non-Markovian quantum kinetic equation which resums the perturbative series and includes off-shell effects. A Markovian approximation that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the limit of wide separation of time scales upon different coarse-graining assumptions. The relaxational dynamics predicted by the non-Markovian, Markovian and Boltzmann approximations are compared to the exact result. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effects are important.