Semiclassical analysis of discontinuous systems: Ray-Splitting Billiards

I will be looking at quantum systems that have metric jump-like discontinuities. For such systems it is expected that a ray-splitting billiard flow replaces the classical billiard flow. I will discuss some examples and counterexamples that show to which extent this is true. I will then present a theorem that allows to deduce quantum ergodicity from a property of a classical dynamics.

(joint work with D. Jakobson and Y. Safarov)