Microlocal Normal Forms for the Magnetic Laplacian
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.

@article{JEDP_2014____A12_0,
     author = {V\~u Ng\d oc, San},
     title = {Microlocal Normal Forms for the Magnetic Laplacian},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2014},
     doi = {10.5802/jedp.115},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_2014____A12_0}
}
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/item/JEDP_2014____A12_0/

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