Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap

TL;DR

This study numerically investigates how Bose-Einstein condensates in a Sinai oscillator trap undergo dynamical thermalization due to nonlinear interactions, revealing a transition from quasi-integrable to thermalized states and linking to quantum chaos.

Contribution

It demonstrates the emergence of thermalization in a Sinai oscillator trap modeled by the Gross-Pitaevskii equation, connecting quantum chaos with Bose-Einstein condensate dynamics.

Findings

Thermalization occurs above a certain interaction threshold.

Below the threshold, evolution remains quasi-integrable.

The system can serve as an experimental test bed for thermalization studies.

Abstract

We study numerically the evolution of Bose-Einstein condensate in the Sinai oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border the evolution remains quasi-integrable. Such a Sinai oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in rst experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.