[Etat fondamental de l'opérateur de Schrödinger avec champ magnétique dans un domaine à coin]
Nous démontrons que la réalisation de Neumann de l'opérateur de Schrödinger avec un champ magnétique constant sur un secteur d'angle α∈]0,π] admet au moins une valeur propre, en dessous du spectre essentiel, quand l'angle est suffisamment petit. Nous établissons un développement limité de la plus petite valeur propre pour α proche de 0. Cette étude permet de donner des estimations du bas du spectre dans le cas semi-classique pour des domaines à coin.
We show that the Neumann realization for the Schrödinger operator with a constant magnetic field in a sector has at least one eigenvalue below the essential spectrum, when the angle is sufficiently small. We establish the complete asymptotics of the lowest eigenvalue as the angle tends to 0. This study is applied to the analysis of the bottom of the spectrum in the semi-classical case for domains with edges.
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@article{CRMATH_2003__336_2_135_0,
author = {Bonnaillie, Virginie},
title = {On the fundamental state for a {Schr\"odinger} operator with magnetic field in a domain with corners},
journal = {Comptes Rendus. Math\'ematique},
pages = {135--140},
publisher = {Elsevier},
volume = {336},
number = {2},
year = {2003},
doi = {10.1016/S1631-073X(03)00008-6},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(03)00008-6/}
}
TY - JOUR AU - Bonnaillie, Virginie TI - On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners JO - Comptes Rendus. Mathématique PY - 2003 SP - 135 EP - 140 VL - 336 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S1631-073X(03)00008-6/ DO - 10.1016/S1631-073X(03)00008-6 LA - en ID - CRMATH_2003__336_2_135_0 ER -
%0 Journal Article %A Bonnaillie, Virginie %T On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners %J Comptes Rendus. Mathématique %D 2003 %P 135-140 %V 336 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S1631-073X(03)00008-6/ %R 10.1016/S1631-073X(03)00008-6 %G en %F CRMATH_2003__336_2_135_0
Bonnaillie, Virginie. On the fundamental state for a Schrödinger operator with magnetic field in a domain with corners. Comptes Rendus. Mathématique, Tome 336 (2003) no. 2, pp. 135-140. doi : 10.1016/S1631-073X(03)00008-6. http://archive.numdam.org/articles/10.1016/S1631-073X(03)00008-6/
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