Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

Abstract

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.

LaTeX, 19 pages

References in corpus (3)

• Quantum Mechanics and Semiclassics of Hyperbolic n-Disk Scattering Systems
• Semiclassical Interpretation of the Mass Asymmetry in Nuclear Fission
• Quantization of Hyperbolic N-Sphere Scattering Systems in Three Dimensions

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