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 in the direction of the field. In particular, we prove that they are simple.
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 dans la direction du champ. En particulier, nous prouvons la simplicité des valeurs propres.
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Keywords: magnetic Schrödinger operator, semiclassical analysis, eigenvalues
Mot clés : opérateur de Schrödinger magnétique, analyse semiclassique, valeurs propres
Hérau, Frédéric 1; Raymond, Nicolas 2
@article{AIF_2024__74_3_915_0, author = {H\'erau, Fr\'ed\'eric and Raymond, Nicolas}, title = {Semiclassical spectral gaps of the {3D} {Neumann} {Laplacian} with constant magnetic field}, journal = {Annales de l'Institut Fourier}, pages = {915--972}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {3}, year = {2024}, doi = {10.5802/aif.3631}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3631/} }
TY - JOUR AU - Hérau, Frédéric AU - Raymond, Nicolas TI - Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field JO - Annales de l'Institut Fourier PY - 2024 SP - 915 EP - 972 VL - 74 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3631/ DO - 10.5802/aif.3631 LA - en ID - AIF_2024__74_3_915_0 ER -
%0 Journal Article %A Hérau, Frédéric %A Raymond, Nicolas %T Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field %J Annales de l'Institut Fourier %D 2024 %P 915-972 %V 74 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3631/ %R 10.5802/aif.3631 %G en %F AIF_2024__74_3_915_0
Hérau, Frédéric; Raymond, Nicolas. Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field. Annales de l'Institut Fourier, Volume 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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