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

M. Wilkinson

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages75-79
Number of pages5
JournalPhysica Scripta
VolumeT90
DOIs
Publication statusPublished - 2001

Fingerprint

Quantum Chaos
Periodic Orbits
chaos
orbits
Universality
Correlation Function
Random Matrix Theory
Log Normal Distribution
Chaotic System
Statistical property
analytic functions
space density
Phase Space
Analytic function
matrix theory
Correspondence
Bifurcation
Orbit
normal density functions
Statistics

Keywords

  • chaotic classical dynamics
  • periodic orbit
  • random matrix theory
  • quantum statistics

Cite this

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Non-universality of chaotic classical dynamics : implications for quantum chaos. / Wilkinson, M.

In: Physica Scripta, Vol. T90, 2001, p. 75-79.

Research output: Contribution to journalArticle

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AB - 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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