Transition From Poissonian TO Gaussian-orthogonal-ensemble Level Statistics IN A Modified Artins Billiard

Abstract

One wall of an Artin's billiard on the Poincare half-plane is replaced by a one-parameter (c(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 c(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 c(p)=1: A finite-size scaling relation for the Brody parameter as a function of 1-c(p) and the number of levels considered can be established.