Weyl law for semi-classical resonances with randomly perturbed potentials
Mémoires de la Société Mathématique de France, no. 136 (2014), 150 p.
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We consider semi-classical Schrödinger operators with potentials supported in a bounded strictly convex subset 𝒪 of n with smooth boundary. Letting h denote the semi-classical parameter, we consider 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 𝒪 up to a small remainder.

On considère des opérateurs de Schrödinger dont les potentiels ont leur supports dans un ensemble strictement convexe à bord lisse 𝒪 n . En désignant par h le paramètre semi-classique, nous considérons des classes de petites perturbations aléatoires et montrons qu’avec une probabilité très proche de 1, le nombre de résonances dans des rectangles [a,b]-i[0,ch 2 3 [ est égal (à un petit reste près) au nombre de valeurs propres dans [a,b] de la réalisation de Dirichlet de l’opérateur dans 𝒪.

DOI : https://doi.org/10.24033/msmf.446
Classification:  81U99,  35P20,  35P25
Keywords: Resonance, Weyl law, Random
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     author = {Sj\"ostrand, Johannes},
     title = {Weyl law for semi-classical resonances with randomly perturbed potentials},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {136},
     year = {2014},
     doi = {10.24033/msmf.446},
     zbl = {1304.35010},
     mrnumber = {3288114},
     language = {en},
     url = {http://www.numdam.org/item/MSMF_2014_2_136__1_0}
}
Sjöstrand, Johannes. Weyl law for semi-classical resonances with randomly perturbed potentials. Mémoires de la Société Mathématique de France, Serie 2, , no. 136 (2014), 150 p. doi : 10.24033/msmf.446. http://www.numdam.org/item/MSMF_2014_2_136__1_0/

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