Curvature induced magnetic bound states: towards the tunneling effect for the ellipse

Virginie Bonnaillie-Noël (1) , Frédéric Hérau (2) , Nicolas Raymond (3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 IRMAR - Institut de Recherche Mathématique de Rennes

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 in generic situations. We also explain and illustrate a conjecture of magnetic tunneling when the domain is an ellipse.

Domaines: Mathématiques [math]

Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond. Curvature induced magnetic bound states: towards the tunneling effect for the ellipse. 2017. ⟨hal-01404924v2⟩