Non-equilibrium dynamics of Gaudin models

¹ Department of Theoretical Physics, University of Geneva, 24 - Quai Ernest-Ansermet, 1211 Genève 4, Switzerland
² Physics Department, University of Fribourg - Chemin du Musée 3, 1700 Fribourg, Switzerland
³ Institute for Theoretical Physics, University of Amsterdam - Science Park 904, Postbus 94485, 1098 XH Amsterdam, The Netherlands

Received: 18 September 2013
Accepted: 8 October 2013

Abstract

In classical mechanics the theory of non-linear dynamics provides a detailed framework for the distinction between near-integrable and chaotic systems. Quite in opposition, in quantum many-body theory no generic microscopic principle at the origin of complex dynamics is known. Here we show that the non-equilibrium dynamics of homogeneous Gaudin models can be fully described by underlying classical Hamiltonian equations of motion. The original Gaudin system remains fully quantum and thus cannot exhibit chaos, but the underlying classical description can be analyzed using the powerful tools of the classical theory of motion. We specifically apply this strategy to the Tavis-Cummings model for quantum photons interacting with an ensemble of two-level systems. We show that scattering in the classical phase space can drive the quantum model close to thermal equilibrium. Interestingly, this happens in the fully quantum regime, where physical observables do not show any dynamic chaotic behavior.