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Non-universality of chaotic classical dynamics: implications for quantum chaos

Wilkinson, M. (2001) Non-universality of chaotic classical dynamics: implications for quantum chaos. Physica Scripta, T90. pp. 75-79. ISSN 0031-8949

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    Abstract

    It might be anticipated that there is statistical universality in the long-time classical dynamics of chaotic systems, corresponding to the universal agreement between their quantum spectral statistics and random matrix theory. It is argued that no such universality exists. Two statistical properties of long period orbits are considered. The distribution of the phase-space density of periodic orbits of fixed length is shown to have a log-normal distribution. Also, a correlation function of periodic-orbit actions is discussed, which has a semiclassical correspondence to the quantum spectral two-point correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodic-orbit actions. They lead to a result which is non-universal, and which in general may not be an analytic function of the action difference.

    Item type: Article
    ID code: 6443
    Keywords: chaotic classical dynamics, periodic orbit, random matrix theory, quantum statistics, Physics
    Subjects: Science > Physics
    Department: Unknown Department
    Related URLs:
    Depositing user: Miss Darcy Spiller
    Date Deposited: 01 Jul 2008
    Last modified: 24 Sep 2011 18:52
    URI: http://strathprints.strath.ac.uk/id/eprint/6443

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