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