Canal-U

San VuNgoc - Symplectic normal forms and spectral asymptotics for magnetic fields in 3D

I will present recent results giving precise eigenvalue asymptotics for the magnetic Laplacian for large magnetic  fields (semiclassical limit),  in the case of a con ning,  non-uniform field, in dimension 3.  The essential ingredient is the symplectic geometry of the zero-energy manifold in the magnetic phase space.  Under natural conffinement assumptions for the magnetic  field, one can perform three successive normal forms corresponding to three physical
scales of oscillations.

This is joint work with B. Hel er, Y. Kordyukov and N. Raymond.