Quantum chaos and effective thermalization

TL;DR

This paper investigates how quantum systems exhibit effective thermalization under classical chaos, using the Dicke model and phase-space methods to describe the process as a balance of drift and diffusion.

Contribution

It provides a constructive phase-space framework for understanding quantum thermalization in chaotic systems, highlighting the role of Fokker-Planck dynamics.

Findings

Effective equilibration demonstrated in the Dicke model.

Thermalization described by a Fokker-Planck equation.

Quantum diffusion smoothens classical singularities.

Abstract

We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber $Q$ or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a 'quantum smoothened' approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.