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Random matrix theory within superstatistics

Statistical Mechanics 2007-05-23 v1

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.

Keywords

Cite

@article{arxiv.cond-mat/0510494,
  title  = {Random matrix theory within superstatistics},
  author = {A. Y. Abul-Magd},
  journal= {arXiv preprint arXiv:cond-mat/0510494},
  year   = {2007}
}

Comments

20 pages, 6 figures