Kinetics of the disordered Bose gas with collisions

TL;DR

This paper develops a kinetic theory framework for the disordered interacting Bose gas, unifying various results and exploring how interactions influence localization and wave packet spreading during expansion.

Contribution

It introduces a Boltzmann transport equation approach to analyze the dynamics of disordered Bose gases, generalizing previous microscopic models and addressing interaction effects on localization.

Findings

Transport theory reproduces known microscopic results.

Interaction effects can cause wave packet expansion beyond localization length.

Collision-induced diffusion describes the spreading in the large particle number regime.

Abstract

We discuss the kinetics of the disordered interacting Bose gas using the Boltzmann transport equation. The theory may serve as a unifying framework for studying questions of dynamics of the expanding Bose gas at different stages of the expansion. We show that the transport theory allows us to straightforwardly reproduce and generalize a number of results previously obtained from microscopic models in different formalisms. Based on estimates for the interparticle scattering rates, we discuss the relevance of interaction effects for the localization problem in the interacting disordered Bose gas. We argue that, if the number of particles is large enough, the size of the expanding cloud may exceed the localization length. We describe the spreading of the wave packet in this regime as collision-induced diffusion and compare the obtained rate of expansion to known results on subdiffusive spreading in nonlinear disordered lattices.