Non-equilibrium dynamics of Gaudin models

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. In this paper, the authors 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. The authors specifically apply this strategy to the Tavis-Cummings model for quantum photons interacting with an ensemble of two-level systems. They 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.