Curvature induced magnetic bound states: towards the tunneling effect for the ellipse
Bonnaillie-Noël, Virginie1; Hérau, Frédéric2; Raymond, Nicolas3
1 DMA - UMR CNRS 8553 PSL Research University CNRS, ENS Paris 45 rue d’Ulm F-75230 Paris cedex 05, France
2 LMJL - UMR CNRS 6629 Université de Nantes, CNRS 2 rue de la Houssinière BP 92208 F-44322 Nantes cedex 3, France
3 IRMAR - UMR CNRS 8625 Université Rennes 1, CNRS Campus de Beaulieu F-35042 Rennes cedex, France
Journées équations aux dérivées partielles (2016), Talk no. 3, 14 p.

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.

Published online:
DOI: 10.5802/jedp.644
Bonnaillie-Noël, Virginie 1; Hérau, Frédéric 2; Raymond, Nicolas 3

1 DMA - UMR CNRS 8553 PSL Research University CNRS, ENS Paris 45 rue d’Ulm F-75230 Paris cedex 05, France
2 LMJL - UMR CNRS 6629 Université de Nantes, CNRS 2 rue de la Houssinière BP 92208 F-44322 Nantes cedex 3, France
3 IRMAR - UMR CNRS 8625 Université Rennes 1, CNRS Campus de Beaulieu F-35042 Rennes cedex, France 
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     title = {Curvature induced magnetic bound states:  towards the tunneling effect for the ellipse},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
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     publisher = {Groupement de recherche 2434 du CNRS},
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Bonnaillie-Noël, Virginie; Hérau, Frédéric; Raymond, Nicolas. 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. http://www.numdam.org/articles/10.5802/jedp.644/

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