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.
@incollection{JEDP_2014____A12_0, author = {San V\~{u} Ngọc}, title = {Microlocal {Normal} {Forms} for the {Magnetic} {Laplacian}}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {12}, pages = {1--12}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2014}, doi = {10.5802/jedp.115}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.115/} }
TY - JOUR AU - San Vũ Ngọc TI - Microlocal Normal Forms for the Magnetic Laplacian JO - Journées équations aux dérivées partielles PY - 2014 SP - 1 EP - 12 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.115/ DO - 10.5802/jedp.115 LA - en ID - JEDP_2014____A12_0 ER -
%0 Journal Article %A San Vũ Ngọc %T Microlocal Normal Forms for the Magnetic Laplacian %J Journées équations aux dérivées partielles %D 2014 %P 1-12 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.115/ %R 10.5802/jedp.115 %G en %F JEDP_2014____A12_0
San Vũ Ngọc. Microlocal Normal Forms for the Magnetic Laplacian. Journées équations aux dérivées partielles (2014), article no. 12, 12 p. doi : 10.5802/jedp.115. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.115/
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