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 , where the authors proved the equidistribution result under a similar assumption on fixed points but with the condition that there is no trapping.
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Maxime Ingremeau, Equidistribution of phase shifts in trapped scattering. J. Spectr. Theory 8 (2018), no. 4, pp. 1199–1220DOI 10.4171/JST/225