Equidistribution of phase shifts in trapped scattering

Abstract

We consider semiclassical scattering for compactly supported perturbations of the Laplacian and show equidistribution of eigenvalues of the scattering matrix at (classically) non-degenerate energy levels. The only requirement is that sets of fixed points of certain natural scattering relations have measure zero. This extends the result of [16], where the authors proved the equidistribution result under a similar assumption on fixed points but with the condition that there is no trapping.