Thermalization in an interacting spin system in the transition from integrability tochaos

Abstract

A stringent analysis of nonequilibrium dynamics and thermalization in a complexinteracting spin system, which transits from integrability to chaos, is performed.The applicability of both standard thermodynamical ensembles—canonical andmicrocanonical—and the generalized Gibbs ensemble is tested. The role of constants ofmotion is studied, and a critical analysis of the usual definition of quantum integrability isperformed. Different possible thermalization mechanisms are also analyzed. We findsignificant discrepancies between the time averages of some observables and theprediction from the thermodynamical ensembles within the ergodic region, so weconclude that quantum chaos does not guarantee thermalization. We also findthat quantum integrable dynamics keeps more memory concerning the initialstate, which is in part stored in a set of constants of motion that can be explicitlyobtained.