A unified time scale for quantum chaotic regimes

TL;DR

This paper introduces a generalized time scale for quantum chaos that unifies various existing scales using nonextensive statistical mechanics, linking quantum phase space properties with chaos regimes.

Contribution

It proposes a novel unified time scale for quantum chaos dynamics derived from nonextensive entropy and phase space graininess, connecting classical and quantum chaos measures.

Findings

Recovering classical and quantum chaos time scales as special cases.

Deriving Lyapunov and regular regimes from a nonextensive correlation function.

Establishing a link between nonextensive entropy and fidelity decay 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.