Classical basis for quantum spectral fluctuations in hyperbolic systems

S Muller*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

18 Citations (Scopus)

Abstract

We reason in support of the universality of quantum spectral fluctuations in chaotic systems; starting from the pioneering work of Sieber and Richter who expressed the spectral form factor in terms of pairs of periodic orbits with self-crossings and avoided crossings. Dropping the restriction to uniformly hyperbolic dynamics; we show that for general hyperbolic two-freedom systems with tune-reversal invariance the spectral form factor is faithful to random-matrix theory; up to quadratic order in time. We relate the action difference within the contributing pairs of orbits to properties of stable and unstable manifolds. In studying the effects of conjugate points, we show that almost self-retracing orbit loops do not contribute to the form factor. Our findings are substantiated by numerical evidence for the concrete example of two billiard systems.

Original languageEnglish
Pages (from-to)305-319
Number of pages15
JournalEuropean Physical Journal B: Condensed Matter
Volume34
Issue number3
DOIs
Publication statusPublished - Aug 2003

Keywords

  • MASLOV INDEXES
  • CARDIOID BILLIARD
  • TIME-REVERSAL
  • DENSITY
  • TRACE FORMULA
  • STATISTICS
  • PERIODIC-ORBITS
  • QUANTIZATION
  • PENUMBRA DIFFRACTION
  • FORM-FACTOR

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