Weyl law for semi-classical resonances with randomly perturbed potentials

Abstract

In this work we consider semi-classical Schrödinger operators with potentials supported in a bounded strictly convex subset $\mathcal{O}$ of ${\mathbf{R}}^n$ 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 $[a,b]-i[0,c{h}^{2/3}[$, is equal to the number of eigenvalues in $[a,b]$ of the Dirichlet realization of the unperturbed operator in $\mathcal{O}$ up to a small remainder.

Revised version, accepted for publication

References in corpus (1)

• Bohr-Sommerfeld quantization condition for non-selfadjoint operators in dimension 2

Cited by in corpus (1)

• Resonances and Spectral Shift Function Singularities for Magnetic Quantum Hamiltonians