Microlocal Normal Forms for the Magnetic Laplacian | Zendy

San Vũ Ngọc | Zendy

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Microlocal Normal Forms for the Magnetic Laplacian

Author(s) -

San Vũ Ngọc

Publication year - 2014

Publication title -

journées équations aux dérivées partielles

Language(s) - English

Resource type - Journals

eISSN - 2118-9366

pISSN - 0752-0360

DOI - 10.5802/jedp.115

Subject(s) - differential operator , laplace operator , microlocal analysis , eigenvalues and eigenvectors , mathematics , semiclassical physics , operator (biology) , symplectic geometry , mathematical analysis , pure mathematics , fourier integral operator , operator theory , physics , quantum mechanics , chemistry , biochemistry , repressor , transcription factor , quantum , gene

Exposé n° XIIInternational audienceWe 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

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