Semiclassical analysis of spectral correlations in regular billiards with point scatterers

Olivier Legrand, Fabrice Mortessagne, Richard L. Weaver

Research output: Contribution to journalArticlepeer-review

Abstract

A semiclassical analysis is proposed to elucidate quantitatively the deviations from the predictions of the random matrix theory of the observed conditional number density in rectangular billiards with point scatterers [R. L. Weaver and D. Sornette, Phys. Rev. E 52, 3341 (1995)]. Using the scattering cross section of the point scatterer, the spectral form factor is shown to be built on two categories of periodic orbits depending whether they are scattered or not. Our quantitative predictions are successfully compared to the observed spectral correlations in various cases of a rectangular billiard with one or several point scatterers.

Original languageEnglish (US)
Pages (from-to)7741-7744
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number6
DOIs
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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