Nonextensive and superstatistical generalizations of random-matrix theory
Faculty of Engineering Sciences, Sinai University, 068 El Arish, Egypt
Corresponding author: a email@example.com
Revised: 20 January 2009
Published online: 5 May 2009
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.-w – Quantum mechanics / 02.30.Mv – Approximations and expansions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009