Effects of bifurcations on the energy level statistics for oval billiards

H. Makino, T. Harayama, Y. Aizawa

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


We studied the energy level statistics for one parameter family of oval billiards whose classical phase space consists of some regular and some irregular components. As the parameter is varied, a transition from an integrable system to a strongly chaotic one occurs with successive bifurcations. We applied the Berry-Robnik formula to the level-spacing distributions for a variety of shapes of quantum oval billiards and found some striking effects of bifurcations in the classical mechanical systems on the level-spacing distributions. The validity of the Berry-Robnik formula is also checked for those shapes of the oval billiard for which there exist two separated chaotic components in the phase space.

Original languageEnglish
Pages (from-to)4026-4035
Number of pages10
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number4
Publication statusPublished - 1999 Jan 1
Externally publishedYes

ASJC Scopus subject areas

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


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