Nonextensive and superstatistical generalizations of random-matrix theory

Details Nonextensive and superstatistical generalizations of random-matrix theory Nonextensive and superstatistical generalizations of random-matrix theory

2009-02-17

arxiv.org/abs/0902.2943v1

Eur. Phys. J. B 70, 39 (2009)

Physics

Condensed Matter

Statistical Mechanics

25 pages, 2 figures

Scientific paper

10.1140/epjb/e2009-00153-0

Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep base invariance on the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or following the basic prescription of the recently suggested concept of superstatistics. We review these generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments and numerical-experiments on systems in transition from order to chaos.

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