MAGNETIC WKB CONSTRUCTIONS ON SURFACES

Yannick Guedes Bonthonneau (1) , Tho Nguyen Duc (1) , Nicolas Raymond (2) , San Vu Ngoc (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumption that the magnetic field has a unique and non-degenerate minimum, we construct the local complex WKB approximations for eigenfunctions on a general surface. Furthermore, in the case of the Euclidean plane, with a radially symmetric magnetic field, the eigenfunctions are approximated in an exponentially weighted space.

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Yannick Guedes Bonthonneau, Tho Nguyen Duc, Nicolas Raymond, San Vu Ngoc. MAGNETIC WKB CONSTRUCTIONS ON SURFACES. Reviews in Mathematical Physics, In press, pp.article n° 2150022. ⟨10.1142/S0129055X2150022⟩. ⟨hal-02493695⟩