### Abstract

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 language | English |
---|---|

Pages (from-to) | 4026-4035 |

Number of pages | 10 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 59 |

Issue number | 4 |

Publication status | Published - 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*59*(4), 4026-4035.

**Effects of bifurcations on the energy level statistics for oval billiards.** / Makino, H.; Harayama, Takahisa; Aizawa, Y.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 4, pp. 4026-4035.

}

TY - JOUR

T1 - Effects of bifurcations on the energy level statistics for oval billiards

AU - Makino, H.

AU - Harayama, Takahisa

AU - Aizawa, Y.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001376454&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001376454&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001376454

VL - 59

SP - 4026

EP - 4035

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

ER -