On the Semiclassical Magnetic Laplacian and Connected Topics

Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The aim of this course is to introduce the reader to the general techniques appearing in the spectral theory of the semiclassical magnetic Laplacian. We explain how we can construct quasi-eigenpairs and how the investigation of the magnetic Laplacian can be reduced to the one of model operators. In particular, the localization estimates of Agmon and the Born-Oppenheimer approximation are discussed in this course. We also propose to analyze two recent examples and we finally provide some other perspectives (Birkhoff normal form and semiclassical waveguides).

Mots clés: Magnetic Laplacian; Semiclassical Analysis; Spectral Theory; Agmon estimates; Waveguides; Normal Form

Domaines: Physique mathématique [math-ph]

Nicolas Raymond. On the Semiclassical Magnetic Laplacian and Connected Topics. 2012. ⟨hal-00725923v2⟩