On the ground state energy for a magnetic Schrödinger operator and the effect of the de Gennes boundary condition

Ayman Kachmar

doi:10.1016/j.crma.2006.03.001

Mathematical Physics

On the ground state energy for a magnetic Schrödinger operator and the effect of the de Gennes boundary condition

Presented by: Jean-Michel Bony

Ayman Kachmar ^1,²

¹ Université Paris-Sud, département de mathématiques, bâtiment 425, 91405 Orsay, France
² Université Libanaise, département de mathématiques, Hadeth, Beyrouth, Lebanon

Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 701-706.

Abstract
Résumé

Motivated by the Ginzburg–Landau theory of superconductivity, we estimate the ground state energy of a magnetic Schrödinger operator with de Gennes boundary condition in the semi-classical limit and we study the localization of the corresponding ground states. We exhibit cases when the de Gennes boundary condition has a strong effect on this localization.

Motivé par la théorie de Ginzburg–Landau de supraconductivité, nous estimons dans le régime semi-classique l'énergie de l'état fondamental d'un opérateur de Schrödinger avec champ magnétique et condition au bord de de Gennes. Nous obtenons des cas où la condition au bord de de Gennes a un effet fort sur cette localisation.

Received: 2006-01-12
Accepted: 2006-02-28
Published online: 2006-03-31

DOI: 10.1016/j.crma.2006.03.001

Author's affiliations:

Ayman Kachmar ^{1, 2}

¹ Université Paris-Sud, département de mathématiques, bâtiment 425, 91405 Orsay, France
² Université Libanaise, département de mathématiques, Hadeth, Beyrouth, Lebanon

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     author = {Ayman Kachmar},
     title = {On the ground state energy for a magnetic {Schr\"odinger} operator and the effect of the de {Gennes} boundary condition},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {701--706},
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     year = {2006},
     doi = {10.1016/j.crma.2006.03.001},
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Ayman Kachmar. On the ground state energy for a magnetic Schrödinger operator and the effect of the de Gennes boundary condition. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 701-706. doi : 10.1016/j.crma.2006.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.001/

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