Quantum Chaos in Systems with Ray Splitting

We extend results of quantum chaos to systems which support multiple wave types that are coupled by reflection at boundaries. We first consider the example of a bounded two-dimensional elastic region, and obtain numerical results for the limiting classical system which shows an enhanced tendency for ergodicity in systems with ray splitting as compared to systems without ray splitting. We then consider the semiclassical limit and develop the following results for systems with ray splitting: (a) an expression for the path sum approximation of the Green function, (b) an order of magnitude sum rule for the amplitudes of the path sum of the density of states, (c) an expression for the Delta_3 statistic of the density of states, and (d) an estimate of the effects of scars on the band-averaged magnitude-squared of the wave function.