Microlocal Normal Forms for the Magnetic Laplacian

San Vũ Ngọc (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We explore symplectic techniques to obtain long time estimates for a purely magnetic confinement in two degrees of freedom. Using pseudo-differential calculus, the same techniques lead to microlocal normal forms for the magnetic Laplacian. In the case of a strong magnetic field, we prove a reduction to a 1D semiclassical pseudo-differential operator. This can be used to derive precise asymptotic expansions for the eigenvalues at any order.

Domaines: Equations aux dérivées partielles [math.AP]

San Vũ Ngọc. Microlocal Normal Forms for the Magnetic Laplacian. Equations aux dérivées partielles, Jun 2014, Roscoff, France. pp.1 - 12, ⟨10.5802/jedp.115⟩. ⟨hal-01416632⟩