Chaoticity without thermalisation in disordered lattices

TL;DR

This paper investigates how disorder in lattices affects chaos and thermalization in Bose-Einstein condensates, revealing that disorder prevents ergodicity and challenges the use of Lyapunov exponents as thermalization indicators.

Contribution

It demonstrates that disorder breaks phase space into disjoint regions, making Lyapunov exponents unreliable for predicting thermalization in disordered BEC systems.

Findings

Disorder destroys ergodicity by fragmenting phase space.

Lyapunov exponents are poor indicators of thermalization.

Classical localization does not occur despite disorder.

Abstract

We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schr\"odinger equation (DNLS). A symplectic integration method allows us to accurately obtain both the full phase space trajectories and their maximum Lyapunov exponents (mLEs), which characterize their chaoticity. We find that disorder destroys ergodicity by breaking up phase space into subsystems that are effectively disjoint on experimentally relevant timescales, even though energetically, classical localisation cannot occur. This leads us to conclude that the mLE is a very poor ergodicity indicator, since it is not sensitive to the trajectory being confined to a subregion of phase space. The eventual thermalization of a BEC in a disordered lattice cannot be predicted based only on the chaoticity of its phase space trajectory.