Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime

TL;DR

This paper develops a nonextensive random matrix theory using Tsallis entropy to model systems with mixed regular and chaotic dynamics, providing analytical level-spacing distributions for small matrices and validating them numerically.

Contribution

It introduces a novel RMT framework based on Tsallis entropy for super-extensive regimes, extending traditional RMT to complex dynamical systems.

Findings

Analytical level-spacing distributions derived for 2x2 matrices.

Numerical validation with harmonic oscillator models.

Extension of RMT to super-extensive nonextensive regimes.

Abstract

We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical expressions for the level-spacing distributions, which are strictly valid for 2 \times 2 random-matrix ensembles, as usually done in the standard RMT. We compare the results with spacing distributions, numerically calculated for random matrix ensembles describing a harmonic oscillator perturbed by Gaussian orthogonal and unitary ensembles.