Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

Details Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards Periodic Orbits and Spectral Statistics of Pseudointegrable Billiards

1996-08-28

arxiv.org/abs/chao-dyn/9608017v1

Phys. Rev. E 54 (1996) R1044

Nonlinear Sciences

Chaotic Dynamics

13 pages in RevTex including 5 figures

Scientific paper

10.1103/PhysRevE.54.R1044

We demonstrate for a generic pseudointegrable billiard that the number of periodic orbit families with length less than $l$ increases as $\pi b_0l^2/\langle a(l) \rangle$, 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.

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