Abstract
We study the classical and quantum mechanics of a three-dimensional stadium billiard. It consists of two quarter cylinders that are rotated with respect to each other by 90 degrees, and it is classically chaotic. The billiard exhibits only a few families of non-generic periodic orbits. We introduce an analytic method for their treatment. The length spectrum can be understood in terms of the non-generic and unstable periodic orbits. For unequal radii of the quarter cylinders, the level statistics agree well with predictions from random matrix theory. For equal radii, the billiard exhibits an additional symmetry. We investigated the effects of symmetry breaking on spectral properties. Moreover, for equal radii, we observe a small deviation of the level statistics from random matrix theory. This led to the discovery of stable orbits which are absent for unequal radii.
