We investigate the semiclassical energy spectrum of quantum ellipticbilliard. The nearest neighbor spacing distribution, level number variance andspectral rigidity support the notion that the elliptic billiard is a genericintegrable system. However, second order statistics exhibit a novel property oflong-range oscillations. Classical simulation shows that all the periodicorbits except two are not isolated. In Fourier analysis of the spectrum, allthe peaks correspond to periodic orbits. The two isolated periodic orbits havesmall contribution to the fluctuation of level density, while non-isolatedperiodic orbits have the main contribution. The heights of the majority of thepeaks match our semiclassical theory except for type-O periodic orbits.Elliptic billiard is a nontrivial integrable system that will enrich ourunderstanding of integrable systems.
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