no. 3
Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field
[Trou spectral semiclassique pour le Laplacien Neumann 3D avec un champ magnétique constant]
Hérau, Frédéric1 ; Raymond, Nicolas2
1 Nantes Université, CNRS, LMJL 2 rue de la Houssinière, BP 92208 44322 Nantes cedex 3 (France)
2 Univ Angers, CNRS, LAREMA, SFR MATHSTIC 49000 Angers (France)
Annales de l'Institut Fourier, Tome 74 (2024) no. 3, pp. 915-972.

Cet article traite de l’analyse spectrale semiclassique du Laplacien magnétique sur un ouvert borné et régulier en dimension trois. Lorsque le champ magnétique est constant, nous établissons un développement asymptotique à cinq termes des plus petites valeurs propres. Ce dernier met en jeu une quantité géométrique définie le long du contour apparent de Ω dans la direction du champ. En particulier, nous prouvons la simplicité des valeurs propres.

This article deals with the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and in the semiclassical limit, we establish a five-term asymptotic expansion of the low-lying eigenvalues, involving a geometric quantity along the apparent contour of Ω in the direction of the field. In particular, we prove that they are simple.

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DOI : 10.5802/aif.3631
Classification : 35PXX, 81Q10, 81Q20
Keywords: magnetic Schrödinger operator, semiclassical analysis, eigenvalues
Mot clés : opérateur de Schrödinger magnétique, analyse semiclassique, valeurs propres
Hérau, Frédéric 1 ; Raymond, Nicolas 2

1 Nantes Université, CNRS, LMJL 2 rue de la Houssinière, BP 92208 44322 Nantes cedex 3 (France)
2 Univ Angers, CNRS, LAREMA, SFR MATHSTIC 49000 Angers (France)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     journal = {Annales de l'Institut Fourier},
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Hérau, Frédéric; Raymond, Nicolas. Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field. Annales de l'Institut Fourier, Tome 74 (2024) no. 3, pp. 915-972. doi : 10.5802/aif.3631. https://aif.centre-mersenne.org/articles/10.5802/aif.3631/

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