Random matrix theory within superstatistics

Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Dec;72(6 Pt 2):066114. doi: 10.1103/PhysRevE.72.066114. Epub 2005 Dec 13.

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 systems in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.