Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime
Mathematical Physics
2011-12-06 v1 Statistical Mechanics
math.MP
Abstract
We apply Tsallis's q-indexed nonextensive entropy to formulate a random matrix theory (RMT), which may be suitable for systems with mixed regular-chaotic dynamics. We consider the super-extensive regime of q < 1. We obtain analytical expressions for the level-spacing distributions, which are strictly valid for 2 \times 2 random-matrix ensembles, as usually done in the standard RMT. We compare the results with spacing distributions, numerically calculated for random matrix ensembles describing a harmonic oscillator perturbed by Gaussian orthogonal and unitary ensembles.
Cite
@article{arxiv.1112.0173,
title = {Random matrix theory for mixed regular-chaotic dynamics in the super-extensive regime},
author = {A. Abd El-Hady and A. Y. Abul-Magd},
journal= {arXiv preprint arXiv:1112.0173},
year = {2011}
}
Comments
9 pages, 5 figures, contribution to the Fifth Saudi Physical Society Meeting