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 $\pi b_0{l}^2/⟨a(l)⟩$, where $b_0$ is a constant and $⟨a(l)⟩$ is the average area occupied by these families. We also find that $⟨a(l)⟩$ 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.

13 pages in RevTex including 5 figures