Random matrix theory within superstatistics

TL;DR

This paper extends random matrix theory by incorporating superstatistics, allowing spectral properties of systems with mixed dynamics to be modeled as averages over stochastic mean level spacings, with applications to transition from order to chaos.

Contribution

It introduces a superstatistical generalization of random matrix theory to describe systems with mixed regular and chaotic behavior.

Findings

The method accurately models the level density and spacing distributions during order-chaos transition.

The calculated spacing distribution matches numerical results from random binary network experiments.

The approach provides a unified framework for spectral analysis in complex systems.

Abstract

We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions and the two-level correlation functions for system in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.