Quantum chaos in systems with ray splitting

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Abstract
We consider wave systems in which rays split on reflection from sharp boundaries. Examples include the Schrödinger equation with the potential changing discontinuously across a surface, electromagnetic waves in a region with a discontinuous dielectric constant, elastic media with a clamped or free boundary, etc. By introducing a Monte Carlo treatment of the rays, it is possible to define chaotic rays via the standard Lyapunov number criterion. Numerical implementation of the Monte Carlo ray technique is carried out for the example of elastic media, and is utilized to investigate the extent to which these systems are globally ergodic. It is suggested that results from previous extensive work on quantum chaos without ray splitting can be extended to these ray splitting problems. In particular, we indicate a generalization of the Gutzwiller trace formula to cover ray splitting.