We investigate the discrete spectrum behaviour for the 2d Pauli operator with nonconstant magnetic field, perturbed by a sign-indefinite self-adjoint electric potential that decays polynomially at infinity. A localisation of the eigenvalues and new asymptotics are established.
Cette note est consacrée à l'étude du comportement des valeurs propres (discrètes) associées à l'opérateur de Pauli 2d en présence d'un champ magnétique non constant et d'un potentiel électrique autoadjoint de signe non fixé qui décroît polynomialement à l'infini. De nouvelles asymptotiques sur les valeurs propres sont obtenues en plus de leur localisation sur le spectre.
Accepted:
Published online:
Diomba Sambou 1; Amal Taarabt 2
@article{CRMATH_2017__355_5_553_0,
author = {Diomba Sambou and Amal Taarabt},
title = {Eigenvalues behaviours for self-adjoint {Pauli} operators with unsigned perturbations and admissible magnetic fields},
journal = {Comptes Rendus. Math\'ematique},
pages = {553--558},
publisher = {Elsevier},
volume = {355},
number = {5},
year = {2017},
doi = {10.1016/j.crma.2017.04.007},
language = {en},
}
TY - JOUR AU - Diomba Sambou AU - Amal Taarabt TI - Eigenvalues behaviours for self-adjoint Pauli operators with unsigned perturbations and admissible magnetic fields JO - Comptes Rendus. Mathématique PY - 2017 SP - 553 EP - 558 VL - 355 IS - 5 PB - Elsevier DO - 10.1016/j.crma.2017.04.007 LA - en ID - CRMATH_2017__355_5_553_0 ER -
%0 Journal Article %A Diomba Sambou %A Amal Taarabt %T Eigenvalues behaviours for self-adjoint Pauli operators with unsigned perturbations and admissible magnetic fields %J Comptes Rendus. Mathématique %D 2017 %P 553-558 %V 355 %N 5 %I Elsevier %R 10.1016/j.crma.2017.04.007 %G en %F CRMATH_2017__355_5_553_0
Diomba Sambou; Amal Taarabt. Eigenvalues behaviours for self-adjoint Pauli operators with unsigned perturbations and admissible magnetic fields. Comptes Rendus. Mathématique, Volume 355 (2017) no. 5, pp. 553-558. doi : 10.1016/j.crma.2017.04.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.007/
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☆ The two authors have been supported by the Chilean Program Núcleo Milenio de Física Matemática RC120002. D. Sambou is supported by the Chilean Fondecyt Grant 3170411. The authors are grateful to J.-F. Bony for his suggestion in the use of the reduction (2.2), G. Raikov for his helpful suggestions during the revision of this note, and the anonymous referee for his helpful remarks, suggestions and comments.
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