Semiclassical theory of strong localization for quantum thermalization

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 $t^{\ast }$, 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.

Comments: 13 pages, 8 figures, improved version with extra figures