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 (https://doi.org/10.1238/Physica.Topical.090a00075)

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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.

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  Item type:	Article
  ID code:	6443
  Dates:	Date Event 2001 Published
  Subjects:	Science > Physics
  Department:	Faculty of Science > Physics
  Depositing user:	Miss Darcy Spiller
  Date deposited:	01 Jul 2008
  Last modified:	11 Nov 2024 08:37
  URI:	https://strathprints.strath.ac.uk/id/eprint/6443