### Abstract

A noncompact, nonintegrable billiard of importance in cosmology-the infinite equilateral triangle on a space of constant negative curvature-gives rise to a natural noncompact integrable approximation, which is studied here quantum mechanically. The Weyl formula for the averaged spectral staircase contains a nonstandard logarithmic term due to the noncompactness of the billiard. For two symmetry classes we determine numerically the spectral staircase, the level-spacing distribution p(s), and the averaged Δ3 statistic, and compare with analytical expressions that follow from Poisson statistics and semiclassical theory. The Poissonian result for the correlation function of Δ3 is derived in closed form and also compared with the data.

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

Pages (from-to) | 7002-7015 |

Number of pages | 14 |

Journal | Physical Review A |

Volume | 44 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1991 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*44*(11), 7002-7015. https://doi.org/10.1103/PhysRevA.44.7002

**Level statistics of a noncompact integrable billiard.** / Graham, Robert; Hübner, Ralph; Szépfalusy, P.; Vattay, G.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 44, no. 11, pp. 7002-7015. https://doi.org/10.1103/PhysRevA.44.7002

}

TY - JOUR

T1 - Level statistics of a noncompact integrable billiard

AU - Graham, Robert

AU - Hübner, Ralph

AU - Szépfalusy, P.

AU - Vattay, G.

PY - 1991

Y1 - 1991

N2 - A noncompact, nonintegrable billiard of importance in cosmology-the infinite equilateral triangle on a space of constant negative curvature-gives rise to a natural noncompact integrable approximation, which is studied here quantum mechanically. The Weyl formula for the averaged spectral staircase contains a nonstandard logarithmic term due to the noncompactness of the billiard. For two symmetry classes we determine numerically the spectral staircase, the level-spacing distribution p(s), and the averaged Δ3 statistic, and compare with analytical expressions that follow from Poisson statistics and semiclassical theory. The Poissonian result for the correlation function of Δ3 is derived in closed form and also compared with the data.

AB - A noncompact, nonintegrable billiard of importance in cosmology-the infinite equilateral triangle on a space of constant negative curvature-gives rise to a natural noncompact integrable approximation, which is studied here quantum mechanically. The Weyl formula for the averaged spectral staircase contains a nonstandard logarithmic term due to the noncompactness of the billiard. For two symmetry classes we determine numerically the spectral staircase, the level-spacing distribution p(s), and the averaged Δ3 statistic, and compare with analytical expressions that follow from Poisson statistics and semiclassical theory. The Poissonian result for the correlation function of Δ3 is derived in closed form and also compared with the data.

UR - http://www.scopus.com/inward/record.url?scp=33947591819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33947591819&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.44.7002

DO - 10.1103/PhysRevA.44.7002

M3 - Article

AN - SCOPUS:33947591819

VL - 44

SP - 7002

EP - 7015

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 11

ER -