Chaoticity without thermalisation in disordered lattices

¹ Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Straße 38, D-01187 Dresden, Germany
² Physics Department, Aristotle University of Thessaloniki - GR-54124, Thessaloniki, Greece
³ Department of Mathematics and Applied Mathematics, University of Cape Town - Rondebosch, 7701, South Africa

Received: 8 August 2013
Accepted: 8 January 2014

Abstract

We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schrödinger 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.