[Opérateurs effectifs sur une discontinuité magnétique]
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.
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.
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Keywords: Magnetic Laplacian, discontinuous magnetic field, semiclassical analysis, spectrum
Mot clés : Laplacien magnétique, champ magnétique discontinu, semi-classique, spectre
Søren Fournais 1 ; Bernard Helffer 2 ; Ayman Kachmar 3 ; Nicolas Raymond 4
CC-BY 4.0
@article{JEP_2023__10__917_0,
author = {S{\o}ren Fournais and Bernard Helffer and Ayman Kachmar and Nicolas Raymond},
title = {Effective operators on an attractive magnetic edge},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {917--944},
publisher = {\'Ecole polytechnique},
volume = {10},
year = {2023},
doi = {10.5802/jep.236},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.236/}
}
TY - JOUR AU - Søren Fournais AU - Bernard Helffer AU - Ayman Kachmar AU - Nicolas Raymond TI - Effective operators on an attractive magnetic edge JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 917 EP - 944 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.236/ DO - 10.5802/jep.236 LA - en ID - JEP_2023__10__917_0 ER -
%0 Journal Article %A Søren Fournais %A Bernard Helffer %A Ayman Kachmar %A Nicolas Raymond %T Effective operators on an attractive magnetic edge %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 917-944 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.236/ %R 10.5802/jep.236 %G en %F JEP_2023__10__917_0
Søren Fournais; Bernard Helffer; Ayman Kachmar; Nicolas Raymond. Effective operators on an attractive magnetic edge. Journal de l’École polytechnique — Mathématiques, Tome 10 (2023), pp. 917-944. doi : 10.5802/jep.236. https://jep.centre-mersenne.org/articles/10.5802/jep.236/
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