Boltzmann equation approach to transport in finite modular quantum systems

TL;DR

This paper explores whether the transport dynamics of finite modular quantum systems can be effectively described by a Boltzmann equation, finding limited applicability to specific models through analytical and numerical analysis.

Contribution

It provides the first detailed analysis of the conditions under which Boltzmann equations accurately model transport in finite modular quantum systems.

Findings

Transport behavior can be described by Boltzmann equation in specific models

Applicability of Boltzmann approach is limited to certain finite systems

Analytical and numerical methods confirm the model-dependent validity

Abstract

We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even and especially for finite systems. Inspired by these results we analyze analytically and numerically if and in which sense the dynamics of those systems are in agreement with an appropriate Boltzmann equation. We find that the transport behavior of a certain type of finite modular quantum systems may indeed be described in terms of a Boltzmann equation. However, the applicability of the Boltzmann equation appears to be rather limited to a very specific type of model.