Periodic Orbit Theory Analysis of a Family of Deformed Hemispherical Billiard Systems

Abstract

We present a periodic orbit theory analysis of a novel three-dimensional billiard system, namely a quasispherical cavity with infinite walls along the conical boundary defined by θ=Θ, where θ is the standard polar angle; for Θ=π/2 this reduces to the special case of a hemispherical infinite well, while for Θ=π it is a spherical well with points along the negative z axis excluded. We focus especially on the connections between subsets of the energy eigenvalue space and their contributions to qualitatively different classes of closed orbits.