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.

13 pages, 8 figures, improved version with extra figures

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Cited by in corpus (6)

• Thermalization and its Breakdown for a Large Nonlinear Spin
• Classical route to ergodicity and scarring in collective quantum systems
• Characterization of hybrid quantum eigenstates in systems with mixed classical phasespace
• Many-body dynamical localization and thermalization
• Nonequilibrium many-body quantum dynamics: from full random matrices to real systems
• Arnold web and dynamical tunneling in a four-site Bose-Hubbard model