I will present recent results giving precise eigenvalue asymptotics for the magnetic Laplacian for large magnetic fields (semiclassical limit), in the case of a con ning, non-uniform field, in dimension 3. The essential ingredient is the symplectic geometry of the zero-energy manifold in the magnetic phase space. Under natural conffinement assumptions for the magnetic field, one can perform three successive normal forms corresponding to three physicalscales of oscillations.This is joint work with B. Hel er, Y. Kordyukov and N. Raymond.
Publié le : 2016-10-13
Classification:
laplacian,
sub-riemannian,
Sub-riemannian day 2016,
symplectic normal forms,
spectral asymptotics,
magnetic fields,
3D,
journée sous-riemannienne 2016,
grenoble,
laplacien,
sous-riemannien,
[MATH]Mathematics [math]
@article{medihal-01383705,
author = {Vu Ngoc, San and Bastien, Fanny},
title = {San VuNgoc - Symplectic normal forms and spectral asymptotics for magnetic fields in 3D },
journal = {HAL},
volume = {2016},
number = {0},
year = {2016},
language = {en},
url = {http://dml.mathdoc.fr/item/medihal-01383705}
}
Vu Ngoc, San; Bastien, Fanny. San VuNgoc - Symplectic normal forms and spectral asymptotics for magnetic fields in 3D . HAL, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/medihal-01383705/