A New Window Onto Quantum Chaos

TL;DR

This paper explores the statistical properties of symmetric random matrices with elements from a non-extensive power-law distribution, deriving a generalized level-spacing distribution that interpolates between chaotic and integrable regimes.

Contribution

It introduces a non-extensive Wigner distribution parameterized by q, extending classical random matrix theory to non-extensive statistics.

Findings

Recover classical GOE results as q approaches 1

Derive a generalized non-extensive Wigner distribution

Show the distribution interpolates between chaos and integrability

Abstract

In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian orthogonal ensemble (GOE) results are recovered. The relevant level spacing distribution is derived and one obtains a suitably generalized non-extensive Wigner distribution which depends on the value of the tunable non-extensivity parameter q. This non-extensive Wigner distribution can be seen to be a one-parameter level-spacing distribution that allows one to interpolate between chaotic and nearly integrable regimes.