Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaos

T. H. Seligman; J. J.M. Verbaarschot

doi:10.1088/0305-4470/18/12/020

Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaos

T. H. Seligman
, J. J.M. Verbaarschot

Physics and Astronomy

Mexico Univ.

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

The authors compare semiclassical and quantum mechanical (numerical) results for spectral statistics in the transition from order to chaos in the corresponding classical system. Scale invariant two-dimensional Hamiltonian are discussed and significant discrepancies are found only for level spacings smaller than one average spacing. For the semiclassical limit they use the result of Berry and Robnik (1984) for the nearest-neighbour spacing distribution and the extension of it to the Delta ₃ statistic.

Original language	English
Article number	020
Pages (from-to)	2227-2234
Number of pages	8
Journal	Journal of Physics A: Mathematical and General
Volume	18
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/18/12/020
State	Published - 1985

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title = "Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaos",

abstract = "The authors compare semiclassical and quantum mechanical (numerical) results for spectral statistics in the transition from order to chaos in the corresponding classical system. Scale invariant two-dimensional Hamiltonian are discussed and significant discrepancies are found only for level spacings smaller than one average spacing. For the semiclassical limit they use the result of Berry and Robnik (1984) for the nearest-neighbour spacing distribution and the extension of it to the Delta 3 statistic.",

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N2 - The authors compare semiclassical and quantum mechanical (numerical) results for spectral statistics in the transition from order to chaos in the corresponding classical system. Scale invariant two-dimensional Hamiltonian are discussed and significant discrepancies are found only for level spacings smaller than one average spacing. For the semiclassical limit they use the result of Berry and Robnik (1984) for the nearest-neighbour spacing distribution and the extension of it to the Delta 3 statistic.

AB - The authors compare semiclassical and quantum mechanical (numerical) results for spectral statistics in the transition from order to chaos in the corresponding classical system. Scale invariant two-dimensional Hamiltonian are discussed and significant discrepancies are found only for level spacings smaller than one average spacing. For the semiclassical limit they use the result of Berry and Robnik (1984) for the nearest-neighbour spacing distribution and the extension of it to the Delta 3 statistic.

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U2 - 10.1088/0305-4470/18/12/020

DO - 10.1088/0305-4470/18/12/020

M3 - Article

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JF - Journal of Physics A: Mathematical and General

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Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaos

Abstract

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