Superstatistics in random matrix theory
arXiv:cond-mat/0507034 · doi:10.1016/j.physa.2005.07.019
Abstract
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis invariant but the matrix elements are not statistically independent. Spectral characteristics of the mixed systems are expressed by averaging the corresponding quantities in the standard random-matrix theory over the fluctuations of the inverse variance of the matrix elements. We obtain analytical expressions for the level density and the nearest-neighbor-spacing distributions for four different inverse-variance distributions. The resulting expressions agree with each others for small departures from chaos, measured by an effective non-extensivity parameter. Our results suggest, among other things, that superstatistics is suited only for the initial stage of transition from chaos to regularity.
15 pages, 5 figures
References in corpus (14)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Superstatistics
- Interpretation of the nonextensitivity parameter in some applications of Tsallis statistics and Lévy distributions
- Dynamical foundations of nonextensive statistical mechanics
- Defect turbulence and generalized statistical mechanics
- Dynamical model and nonextensive statistical mechanics of a market index on large time windows
- Generalized statistical mechanics of cosmic rays
- Lagrangian acceleration statistics in turbulent flows
- Superstatistics in hydrodynamic turbulence
- Multi-parameter generalization of nonextensive statistical mechanics
- Random matrix ensembles from nonextensive entropy
- Statistics of 2+ Levels in Even-Even Nuclei
- Non-extensive Random Matrix Theory - A Bridge Connecting Chaotic and Regular Dynamics
- Theory of monolayers with boundaries: Exact results and Perturbative analysis
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