Transition from Poissonian to Gaussian-orthogonal-ensemble level statistics in a modified Artin's billiard

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Abstract

One wall of an Artin's billiard on the Poincaré half-plane is replaced by a one-parameter (cp) family of nongeodetic walls. A brief description of the classical phase space of this system is given. In the quantum domain, the continuous and gradual transition from the Poisson-like to Gaussian-orthogonal-ensemble (GOE) level statistics due to the small perturbations breaking the symmetry responsible for the "arithmetic chaos" at cp=1 is studied. Another GOE→Poisson transition due to the mixed phase space for large perturbations is also investigated. A satisfactory description of the intermediate level statistics by the Brody distribution was found in both cases. The study supports the existence of a scaling region around cp=1. A finite-size scaling relation for the Brody parameter as a function of 1-cp and the number of levels considered can be established.

Original languageEnglish
Pages (from-to)325-332
Number of pages8
JournalPhysical Review E
Volume49
Issue number1
DOIs
Publication statusPublished - Jan 1 1994

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ASJC Scopus subject areas

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

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