Microlocal Normal Forms for the Magnetic Laplacian
Vũ Ngọc, San1
1 IRMAR (UMR CNRS 6625) Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex, France
Journées équations aux dérivées partielles (2014), article no. 12, 12 p.

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.

DOI : 10.5802/jedp.115
Vũ Ngọc, San 1

1 IRMAR (UMR CNRS 6625) Université de Rennes 1 Campus de Beaulieu 35042 Rennes cedex, France 
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Vũ Ngọc, San. Microlocal Normal Forms for the Magnetic Laplacian. Journées équations aux dérivées partielles (2014), article  no. 12, 12 p. doi : 10.5802/jedp.115. http://www.numdam.org/articles/10.5802/jedp.115/

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