Dynamical thermalization of Bose-Einstein condensate in Bunimovich stadium

TL;DR

This paper numerically investigates how a Bose-Einstein condensate in a chaotic stadium billiard undergoes dynamical thermalization, resulting in a Bose-Einstein distribution over eigenmodes, distinct from classical energy equipartition.

Contribution

It demonstrates the emergence of dynamical thermalization in a nonlinear quantum system with a chaotic boundary, revealing a Bose-Einstein distribution in a new context.

Findings

Thermalization occurs above a certain nonlinearity threshold.

The resulting distribution differs from classical energy equipartition.

Potential for experimental observation in cold atom setups.

Abstract

We study numerically the wavefunction evolution of a Bose-Einstein condensate in a Bunimovich stadium billiard being governed by the Gross-Pitaevskii equation. We show that for a moderate nonlinearity, above a certain threshold, there is emergence of dynamical thermalization which leads to the Bose-Einstein probability distribution over the linear eigenmodes of the stadium. This distribution is drastically different from the energy equipartition over oscillator degrees of freedom which would lead to the ultra-violet catastrophe. We argue that this interesting phenomenon can be studied in cold atom experiments.