Ray splitting and quantum chaos

Recent advances in the theory of the quasiclassical approximation for systems that are chaotic in the classical limit are extended to the case of ray splitting, in particular, to the splitting of an incident ray into a reflected and refracted component at a sharp interface. An instructive example is presented and novel results are found. These include evidence for ray split and periodic orbits in the spectral correlations and a new type of ''scarred'' eigenstate based on combining nonisolated periodic orbits whose quasiclassical contributions have a nontrivial phase from total internal reflection.