Geometry and Spectrum in 2D Magnetic Wells

Nicolas Raymond (1) , San Vu Ngoc (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in $\R^2$. It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional Hamiltonians. As a corollary, recent results by Helffer-Kordyukov are extended to higher energies.

Mots clés: magnetic field; normal form; semiclassical analysis; long time dynamics

Domaines: Théorie spectrale [math.SP]; Géométrie symplectique [math.SG]

Nicolas Raymond, San Vu Ngoc. Geometry and Spectrum in 2D Magnetic Wells. Annales de l'Institut Fourier, 2015, 65 (1), pp.137-169. ⟨10.5802/aif.2927⟩. ⟨hal-00836344v2⟩