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High-order level-spacing distributions for mixed systems
Faculty
Science
Year:
2000
Type of Publication:
Article
Pages:
4792-4798
Authors:
SIMBEL, MH, Abul-Magd, AY
DOI:
10.1103/PhysRevE.62.4792
Journal:
PHYSICAL REVIEW E AMERICAN PHYSICAL SOC
Volume:
62
Research Area:
Physics
ISSN
ISI:000089976800044
Keywords :
High-order level-spacing distributions , mixed systems
Abstract:
We apply some of the methods that have been successfully used to describe the nearest-neighbor-spacing distributions of levels of systems with mixed regular-chaotic dynamics to the calculation of high-order spacing distributions. The distributions for chaotic spectra are described in terms of a previously suggested generalization of Wigner's surmise, which assumes that the high-order level repulsion function is given by a product of the zero-order ones and that all of the spacing distributions are nearly Gaussian functions at large spacings. We compare the expressions obtained by the different methods for the next-nearest-neighbor spacing distribution with the outcome of a recently published numerical experiment on systems in transition between order and chaos. We show that the evolution of the shape of that distribution during the transition of the system from a chaotic to a regular regime is slower than the corresponding transition for the nearest-neighbor spacing distribution.
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