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

TL;DR

This paper provides a detailed asymptotic analysis of the low-lying eigenvalues of the 3D Neumann magnetic Laplacian with a constant magnetic field, revealing geometric influences and eigenvalue simplicity.

Contribution

It introduces a four-term asymptotic expansion for eigenvalues of the 3D Neumann magnetic Laplacian under a constant magnetic field, highlighting geometric effects.

Findings

Eigenvalues have a four-term asymptotic expansion

Eigenvalues are proven to be simple

Geometric quantities influence spectral gaps

Abstract

This article deals with 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 four-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 they are simple.