Effective operators on an attractive magnetic edge
[Opérateurs effectifs sur une discontinuité magnétique]
Fournais, Søren1 ; Helffer, Bernard2 ; Kachmar, Ayman3 ; Raymond, Nicolas4
1 Department of Mathematical Sciences, University of Copenhagen Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
2 Nantes Université, Laboratoire Jean Leray Nantes, France
3 Lebanese University, Department of Mathematics Nabatiye, Lebanon
4 Univ Angers, CNRS, LAREMA, Institut Universitaire de France, SFR MATHSTIC F-49000 Angers, France
Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 917-944

The semiclassical Laplacian with discontinuous magnetic field is considered in two dimensions. The magnetic field is sign changing with exactly two distinct values and is discontinuous along a smooth closed curve, thereby producing an attractive magnetic edge. Various accurate spectral asymptotics are established by means of a dimensional reduction involving a microlocal phase space localization allowing to deal with the discontinuity of the field.

Cet article s’intéresse au laplacien avec champ magnétique discontinu dans la limite semi-classique. Le champ est supposé prendre exactement deux valeurs non nulles de signes opposés et changer de signe le long d’une courbe fermée et régulière, la « frontière magnétique ». Nous établissons diverses asymptotiques spectrales à l’aide d’une réduction de dimension mettant en jeu une localisation dans l’espace des phases et permettant de traiter la discontinuité du champ magnétique.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.236
Classification : 81Q20
Keywords: Magnetic Laplacian, discontinuous magnetic field, semiclassical analysis, spectrum
Mots-clés : Laplacien magnétique, champ magnétique discontinu, semi-classique, spectre

Fournais, Søren 1 ; Helffer, Bernard 2 ; Kachmar, Ayman 3 ; Raymond, Nicolas 4

1 Department of Mathematical Sciences, University of Copenhagen Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
2 Nantes Université, Laboratoire Jean Leray Nantes, France
3 Lebanese University, Department of Mathematics Nabatiye, Lebanon
4 Univ Angers, CNRS, LAREMA, Institut Universitaire de France, SFR MATHSTIC F-49000 Angers, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Effective operators on an attractive magnetic edge},
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Fournais, Søren; Helffer, Bernard; Kachmar, Ayman; Raymond, Nicolas. Effective operators on an attractive magnetic edge. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 917-944. doi: 10.5802/jep.236

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