Peter Barmettler, Vladimir Gritsev
In classical mechanics, sufficiently strong non-linearity can deform regular trajectories into irregular ones, although the equations of motions are fully deterministic. The Kolmogorov-Arnold-Moser theorem can give a bound for the breakdown of regular behavior. In quantum many-body theory, even though there exist examples of deterministic dynamical systems which are difficult to be distinguished from random ones, no generic microscopic principle at the origin of complex dynamics is known. In this article, we present a method for solving the dynamics of a rather general class of quantum integrable and nearly integrable systems, which leads to a natural distinction between regular and irregular behavior. The basic idea is, that the dynamics of the integrable quantum system is described by some underlying classical one, which can be analyzed using the powerful tools of classical theory of motion. We apply the approach to the Dicke Hamiltonian subjected to a periodically driven detuning. This represents generic example of a dynamically perturbed integrable model. 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.
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http://arxiv.org/abs/1201.4416
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