Wilkinson, M. (2001) Nonuniversality of chaotic classical dynamics: implications for quantum chaos. Physica Scripta, T90. pp. 7579. ISSN 00318949

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Abstract
It might be anticipated that there is statistical universality in the longtime 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 phasespace density of periodic orbits of fixed length is shown to have a lognormal distribution. Also, a correlation function of periodicorbit actions is discussed, which has a semiclassical correspondence to the quantum spectral twopoint correlation function. It is shown that bifurcations are a mechanism for creating correlations of periodicorbit actions. They lead to a result which is nonuniversal, 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, Atomic and Molecular Physics, and Optics, Mathematical Physics, Condensed Matter Physics 
Subjects:  Science > Physics 
Department:  Unknown Department 
Depositing user:  Miss Darcy Spiller 
Date Deposited:  01 Jul 2008 
Last modified:  27 Mar 2015 01:32 
URI:  http://strathprints.strath.ac.uk/id/eprint/6443 
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