2005/04/14 by A. Y. Abul-Magd · 4 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.71.066207
published as Phys. Rev. E 71, 066207 (2005) · 15 pages, 3 figures
arxiv created 2005/04/14 · openalex publication_date 2005/06/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We apply Tsallis' q -indexed entropy to formulate a nonextensive random matrix theory, which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix-element variance. It keeps the basis invariance of the standard theory but violates the independence of the matrix elements. We consider the subextensive regime of q more than unity in which the transition from the Wigner to the Poisson statistics is expected to start. We calculate the level density for different values of the entropic index. Our results are consistent with an analogous calculation by Tsallis and collaborators. We calculate the spacing distribution for mixed systems with and without time-reversal symmetry. Comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the Poisson statistics.