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Nonextensive random matrix theory approach to mixed regular-chaotic dynamics
Faculty
Science
Year:
2005
Type of Publication:
Article
Pages:
Authors:
Abul-Magd, AY
DOI:
10.1103/PhysRevE.71.066207
Journal:
PHYSICAL REVIEW E AMERICAN PHYSICAL SOC
Volume:
71
Research Area:
Physics
ISSN
ISI:000230275000052
Keywords :
Nonextensive random matrix theory approach , mixed
Abstract:
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.
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