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Random matrix theory within superstatistics

A. Y. Abul-Magd
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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.

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BibTeXRIS

A. Y. Abul-Magd. 2005-10-19. Random matrix theory within superstatistics. https://doi.org/10.1103/physreve.72.066114

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