This article is devoted to the semiclassical analysis of the magnetic Laplacian on a smooth domain of the plane carrying Neumann boundary conditions. We provide WKB expansions of the eigenfunctions when Neumann boundary traps the lowest eigenfunctions near the points of maximal curvature. We also explain and illustrate a conjecture of magnetic tunneling when the domain is an ellipse.
@incollection{JEDP_2016____A3_0, author = {Virginie Bonnaillie-No\"el and Fr\'ed\'eric H\'erau and Nicolas Raymond}, title = {Curvature induced magnetic bound states: towards the tunneling effect for the ellipse}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, note = {talk:3}, pages = {1--14}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2016}, doi = {10.5802/jedp.644}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.644/} }
TY - JOUR AU - Virginie Bonnaillie-Noël AU - Frédéric Hérau AU - Nicolas Raymond TI - Curvature induced magnetic bound states: towards the tunneling effect for the ellipse JO - Journées équations aux dérivées partielles N1 - talk:3 PY - 2016 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.644/ DO - 10.5802/jedp.644 LA - en ID - JEDP_2016____A3_0 ER -
%0 Journal Article %A Virginie Bonnaillie-Noël %A Frédéric Hérau %A Nicolas Raymond %T Curvature induced magnetic bound states: towards the tunneling effect for the ellipse %J Journées équations aux dérivées partielles %Z talk:3 %D 2016 %P 1-14 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.644/ %R 10.5802/jedp.644 %G en %F JEDP_2016____A3_0
Virginie Bonnaillie-Noël; Frédéric Hérau; Nicolas Raymond. Curvature induced magnetic bound states: towards the tunneling effect for the ellipse. Journées équations aux dérivées partielles (2016), Talk no. 3, 14 p. doi : 10.5802/jedp.644. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.644/
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