Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weyl law for semi-classical resonances with randomly perturbed
  potentials   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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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph