BRUNEAU, Vincent; POPOFF, Nicolas

doi:10.1016/j.jfa.2014.11.015

Métadonnées

Licence d’utilisation du document

BRUNEAU, Vincent
Institut de Mathématiques de Bordeaux [IMB]

POPOFF, Nicolas
CPT - E8 Dynamique quantique et analyse spectrale
Centre de Physique Théorique - UMR 7332 [CPT]
Équipe EDP et Physique Mathématique

Langue

Article de revue

Ce document a été publié dans

Journal of Functional Analysis. 2015, vol. 268, n° 5, p. 1277-1307

Elsevier

Résumé en anglais

We consider the three-dimensional Laplacian with a magnetic field created by an infinite rectilinear current bearing a constant current. The spectrum of the associated hamiltonian is the positive half-axis as the range of an infinity of band functions all decreasing toward 0. We make a precise asymptotics of the band function near the ground energy and we exhibit a semi-classical behavior. We perturb the hamiltonian by an electric potential. Helped by the analysis of the band functions, we show that for slow decaying potential, an infinite number of negative eigenvalues are created whereas only finite number of eigenvalues appears for fast decaying potential. Our results show different borderline type conditions that in the case where there is no magnetic field.< Réduire

Mots clés

Perturbation électrique

Laplacien magnétique

Spectral Theory

Analyse asymptotique

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189400

DOI

http://dx.doi.org/10.1016/j.jfa.2014.11.015

Project ANR

INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE - ANR-11-IDEX-0001
ARCHIMEDE / Mathématiques - ANR-11-LABX-0033

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251