Semiclassical theory of strong localization for quantum thermalization

TL;DR

This paper develops a semiclassical framework to understand strong localization phenomena in quantum thermalization, using a minimal Bose-Hubbard model and classical phase space analysis to predict quantum breaktimes.

Contribution

It introduces a novel semiclassical approach linking classical phase space dynamics with quantum localization effects in many-body systems.

Findings

Derived quantum breaktime from classical Fokker-Planck dynamics

Identified the importance of energy shell geometry in localization

Demonstrated strong localization effects in a minimal Bose-Hubbard model

Abstract

We introduce a semiclassical theory for strong localization that may arise in the context of many-body thermalization. As a minimal model for thermalization we consider a few-site Bose-Hubbard model consisting of two weakly interacting subsystems that can exchange particles. The occupation of a subsystem ($x$) satisfies in the classical treatment a Fokker-Planck equation with a diffusion coefficient $D(x)$. We demonstrate that it is possible to deduce from the classical description a quantum breaktime $t^*$, and hence the manifestations of a strong localization effect. For this purpose it is essential to take the geometry of the energy shell into account, and to make a distinction between different notions of phasespace exploration.