Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems

TL;DR

This paper proposes a minimal Fokker-Planck framework to describe thermalization in weakly-coupled mesoscopic subsystems, highlighting diffusive behavior and potential Levy-flight anomalies due to complex dynamics.

Contribution

It introduces a simplified Fokker-Planck model for thermalization in low-dimensional, non-integrable systems, supported by analysis of Bose-Hubbard trimers.

Findings

Chaotic ergodicity leads to diffusive subsystem responses.

Thermalization can be effectively modeled by a Fokker-Planck equation.

Mesoscopic systems may exhibit Levy-flight anomalies due to slow dynamics.

Abstract

We explore a minimal paradigm for thermalization, consisting of two weakly-coupled, low dimensional, non-integrable subsystems. As demonstrated for Bose-Hubbard trimers, chaotic ergodicity results in a diffusive response of each subsystem, insensitive to the details of the drive exerted on it by the other. This supports the hypothesis that thermalization can be described by a Fokker Plank equation. We also observe, however, that Levy-flight type anomalies may arise in mesoscopic systems, due to the wide range of time scales that characterize `sticky' dynamics.