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

Pages (from-to) | 325-332 |

Number of pages | 8 |

Journal | Physical Review E |

Volume | 49 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1994 |

### Fingerprint

### ASJC Scopus subject areas

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