Semiclassical spectral gaps of the 3D Neumann Laplacian with constant magnetic field

Seminar in Analysis

Speaker: Nicolas Raymond (University of Angers).

Abstract: This talk is devoted to the spectral analysis of the semiclassical Neumann magnetic Laplacian on a smooth bounded domain in dimension three. When the magnetic field is constant and in the semiclassical limit, we establish a five-term asymptotic expansion of the low-lying eigenvalues, involving a geometric quantity along the apparent contour of the domain in the direction of the field. In particular, we prove that the eigenvalues are simple.

Joint work with Frédéric Hérau.