A unified time scale for quantum chaotic regimes

Abstract

We present a generalised time scale for quantum chaos dynamics, motivated by nonextensive statistical mechanics. It recovers, as particular cases, the relaxation (Heisenberg) and the random (Ehrenfest) time scales. Moreover, we show that the generalised time scale can also be obtained from a nonextensive version of the Kolmogorov-Sinai entropy by considering the graininess of quantum phase space and a generalised uncorrelation between subsets of the phase space. Lyapunov and regular regimes for the fidelity decay are obtained as a consequence of a nonextensive generalisation of the $m$th point correlation function for a uniformly distributed perturbation in the classical limit.