Thermalization and localization of an oscillating Bose-Einstein condensate in a disordered trap

TL;DR

This paper numerically investigates how a disordered trap affects the thermalization and localization behaviors of an oscillating Bose-Einstein condensate, confirming energy conservation and identifying regimes of algebraic and exponential localization.

Contribution

It demonstrates the numerical verification of energy conservation and explores the transition from thermalization to localization in a disordered Bose-Einstein condensate.

Findings

Energy and particle number are conserved during oscillation.

Disorder induces thermalization from nonequilibrium.

Algebraic and exponential localization regimes are identified.

Abstract

We numerically simulate an oscillating Bose-Einstein condensate in a disordered trap [Phys. Rev. A 82, 033603 (2010)] and the results are in good agreement with the experiment. It allows us to verify that total energy and particle number are conserved in this quantum system. The disorder acts as a medium, which results in a relaxation from nonequilibrium to equilibrium, i.e., thermalization. An algebraic localization is realized when the system approaches the equilibrium, and if the system falls into the regime when the healing length of the condensate exceeds the correlation length of the disorder, exponential Anderson localization is to be observed.