Spectral theory of confining magnetic fields via symplectic geometry

Conférence sur
« La topologie, la géométrie et la dynamique. En l’honneur de François Lalonde »
 août –  septembre 
Conference on
“Topology, Geometry and Dynamics. In honour of François Lalonde”
August  – September , 
Spectral theory of confining magnetic fields via
symplectic geometry
San Vu Ngoc*
[email protected]
I will present recent results giving precise eigenvalue asymptotics for the magnetic Laplacian for large magnetic fields (semiclassical limit), in the case of a confining, non-uniform
field, in dimensions 2 and 3. The essential ingredient is the symplectic geometry of the
zero-energy manifold in the magnetic phase space, and the quantization of the various
oscillations of the Hamiltonian flow for long times.
This is joint work with B. Helffer, Y. Kordyukov and N. Raymond.
* IRMAR,
Université de Rennes, Camput Beaulieu, 35042 Rennes, Cedex, FRANCE.