Dynamical deviation from quantum integrability

Details Dynamical deviation from quantum integrability Dynamical deviation from quantum integrability

2012-01-21

arxiv.org/abs/1201.4416v1

Physics

Mathematical Physics

7+18 pages, 3 figures

Scientific paper

In classical mechanics, sufficiently strong non-linearity can deform regular trajectories into irregular ones, although equations of motions are fully deterministic. The Kolmogorov-Arnold-Moser theorem can give a bound for the breakdown of a regular behavior. In quantum theory, even though there exist examples of deterministic dynamical systems which are difficult to be distinguished from the 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 allows for 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, to which the powerful tools of classical theory of complexity can be applied. At the example of the Dicke model for interaction of wave and matter, 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 the physical observables do not show any dynamic chaotic behavior.

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