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Journal of Spectral Theory

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Volume 8, Issue 4, 2018, pp. 1199–1220
DOI: 10.4171/JST/225

Published online: 2018-07-25

Equidistribution of phase shifts in trapped scattering

Maxime Ingremeau[1]

(1) Université de Strasbourg, France

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.

Keywords: Phase shifts, scattering theory, semiclassical analysis

Ingremeau Maxime: Equidistribution of phase shifts in trapped scattering. J. Spectr. Theory 8 (2018), 1199-1220. doi: 10.4171/JST/225