Weyl law for semi-classical resonances with randomly perturbed potentials

Details Weyl law for semi-classical resonances with randomly perturbed potentials Weyl law for semi-classical resonances with randomly perturbed potentials

2011-11-15

arxiv.org/abs/1111.3549v2

Mathematics

Analysis of PDEs

Many minor corrections

Scientific paper

In this work we consider semi-classical Schr\"odinger operators with potentials supported in a bounded strictly convex subset ${\cal O}$ of ${\bf R}^n$ with smooth boundary. Letting $h$ denote the semi-classical parameter, we consider certain classes of small random perturbations and show that with probability very close to 1, the number of resonances in rectangles $[a,b]-i[0,ch^{2/3}[$, is equal to the number of eigenvalues in $[a,b]$ of the Dirichlet realization of the unperturbed operator in ${\cal O}$ up to a small remainder.

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