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.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics