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Wigner surmise for high-order level spacing distributions of chaotic systems
Faculty
Science
Year:
1999
Type of Publication:
Article
Pages:
5371-5374
Authors:
SIMBEL, MH, Abul-Magd, AY
DOI:
10.1103/PhysRevE.60.5371
Journal:
PHYSICAL REVIEW E AMERICAN PHYSICAL SOC
Volume:
60
Research Area:
Physics
ISSN
ISI:000083870700049
Keywords :
Wigner surmise , high-order level spacing distributions
Abstract:
We suggest an extension of the Wigner surmise for the nearest-neighbor-spacing distribution of energy levels of chaotic systems to include the nth-order spacing distributions. The main assumption is that the conditional probability density of occurrence of a level at a given distance from a fixed level, provided that this distance contains n levels, is expressed in terms of the (n+1)th power of corresponding probability for a distance containing no levels. At large spacings, the nth-order level distributions are assumed to have a Gaussian shape as in the cases covered by the Wigner surmise. The expressions obtained are in good agreement with the results of numerical calculation by means of the random matrix theory for the three universal classes of symmetry. {[}S1063-651X(99)05210-1].
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