Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

Abstract

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $πb_0l^2/\langle a(l) \rangle$, where $b_0$ is a constant and $\langle a(l) \rangle$ is the average area occupied by these families. We also find that $\langle a(l) \rangle$ increases with $l$ before saturating. Finally, we show that periodic orbits provide a good estimate of spectral correlations in the corresponding quantum spectrum and thus conclude that diffraction effects are not as significant in such studies.