Thermalization in closed quantum systems: semiclassical approach

TL;DR

This paper demonstrates how classical chaotic dynamics, modeled via the truncated Wigner approximation, can explain quantum thermalization in a Bose system, linking initial quantum state sampling to thermal equilibrium.

Contribution

It introduces a semiclassical approach using the truncated Wigner approximation to explain quantum thermalization in Bose particles within a double well potential.

Findings

Chaotic classical evolution leads to thermalization of quantum states.

Sampling initial quantum states acts as a statistical ensemble.

The approach bridges quantum and classical descriptions of thermalization.

Abstract

Thermalization in closed quantum systems can be explained either by means of the eigenstate thermalization hypothesis or the concept of canonical typicality. Both concepts are based on quantum mechanical formalism such as spectral properties of the eigenstates or entanglement between subsystems respectively. Here we study the onset of thermalization of Bose particles in a two-band double well potential using the truncated Wigner approximation. This allows us to use the familiar classical formalism to explain quantum thermalization in this system. In particular, we demonstrate that sampling of an initial quantum state plays the role of a statistical mechanical ensemble, while subsequent chaotic classical evolution turns the initial quantum state into the thermal state.