Non-extensive Random Matrix Theory - A Bridge Connecting Chaotic and Regular Dynamics

TL;DR

This paper introduces a non-extensive generalization of random matrix theory using Tsallis entropy, exploring how the spacing distribution varies with the parameter q across different symmetry classes, bridging chaotic and regular dynamics.

Contribution

It proposes a novel non-extensive framework for random matrix theory based on Tsallis entropy, extending classical results to a broader context.

Findings

Spacing distribution depends on q parameter

Generalizes Wigner's surmises for different ensembles

Connects chaotic and regular dynamics through non-extensive statistics

Abstract

We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of Wigner's surmises for ensembles belonging to the orthogonal, unitary and symplectic symmetry universal classes.