One wall of an Artin’s billiard on the Poincaré half-plane is replaced by a one-parameter (${\mathit{c}}_{\mathit{p}}$) 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 ${\mathit{c}}_{\mathit{p}}$=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 ${\mathit{c}}_{\mathit{p}}$=1. A finite-size scaling relation for the Brody parameter as a function of 1-${\mathit{c}}_{\mathit{p}}$ and the number of levels considered can be established.

• Received 21 June 1993

DOI:https://doi.org/10.1103/PhysRevE.49.325