[Asymptotiques spectrales pour des opérateurs magnétiques de Schrödinger avec des potentiels électriques qui décroissent rapidement à l'infini]
On considère l'opérateur de Schrödinger H(V) agissant dans ou avec un champ magnétique constant et un potentiel électrique V qui génériquement décroı̂t à l'infini exponentiellement vite ou est à un support compact. On étudie le comportement asymptotique du spectre discret de H(V) en voisinage des points de la frontière de son spectre essentiel. Si la décroissance de V est gaussienne ou plus rapide ce comportement ne se décrit pas par les formules semi-classiques connues dans le cas où V décroı̂t comme une puissance.
We consider the Schrödinger operator H(V) on or with constant magnetic field, and a class of electric potentials V which typically decay at infinity exponentially fast or have a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H(V) near the boundary points of its essential spectrum. If V decays like a Gaussian or faster, this behaviour is non-classical in the sense that it is not described by the quasi-classical formulas known for the case where V admits a power-like decay.
Accepté le :
Publié le :
Georgi D. Raikov 1 ; Simone Warzel 2
@article{CRMATH_2002__335_8_683_0,
author = {Georgi D. Raikov and Simone Warzel},
title = {Spectral asymptotics for magnetic {Schr\"odinger} operators with rapidly decreasing electric potentials},
journal = {Comptes Rendus. Math\'ematique},
pages = {683--688},
publisher = {Elsevier},
volume = {335},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02554-2},
language = {en},
}
TY - JOUR AU - Georgi D. Raikov AU - Simone Warzel TI - Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials JO - Comptes Rendus. Mathématique PY - 2002 SP - 683 EP - 688 VL - 335 IS - 8 PB - Elsevier DO - 10.1016/S1631-073X(02)02554-2 LA - en ID - CRMATH_2002__335_8_683_0 ER -
%0 Journal Article %A Georgi D. Raikov %A Simone Warzel %T Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials %J Comptes Rendus. Mathématique %D 2002 %P 683-688 %V 335 %N 8 %I Elsevier %R 10.1016/S1631-073X(02)02554-2 %G en %F CRMATH_2002__335_8_683_0
Georgi D. Raikov; Simone Warzel. Spectral asymptotics for magnetic Schrödinger operators with rapidly decreasing electric potentials. Comptes Rendus. Mathématique, Volume 335 (2002) no. 8, pp. 683-688. doi : 10.1016/S1631-073X(02)02554-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02554-2/
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