Semiclassical 3D Neumann Laplacian with variable magnetic field: a toy model

Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we investigate the semiclassical behavior of the lowest eigenvalues of a model Schrödinger operator with variable magnetic field. This work aims at proving an accurate asymptotic expansion for these eigenvalues, the corresponding upper bound being already proved in the general case. The present work also aims at establishing localization estimates for the attached eigenfunctions.

Mots clés: Magnetic Laplacian; semiclassical analysis; spectral theory; Agmon estimates

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Nicolas Raymond. Semiclassical 3D Neumann Laplacian with variable magnetic field: a toy model. Communications in Partial Differential Equations, 2012, 37 (9), pp.1528-1552. ⟨10.1080/03605302.2012.680558⟩. ⟨hal-00621179v4⟩