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 mth point correlation function for a uniformly distributed perturbation in the classical limit.

Algebraic structures and deformed Schrödinger equations from groups entropies

“…The achievement of nonextensive statistics in describing multiple phenomena (where the application of the traditional Boltzmann-Gibbs (BG) statistical mechanics have shown some problems) as anomalous diffusion [1], long-range interactions [2], plasmas [3], quantum tunneling [4], cold atoms [5], onset of chaos [6], quantum chaos scales [7], and measure theory [8] among others, motivated the construction of several approaches of generalized statistical mechanics from which the foundations of the theory have been extended [9,10]. In these advances, many mathematical frameworks associated with generalized statistics have been proposed [11][12][13][14][15].…”