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, Online first, 58 p.

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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Révisé le :
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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) 
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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, Online first, 58 p.

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