Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)
arXiv:2108.03964 · doi:10.2140/apde.2024.17.535
Abstract
We establish accurate eigenvalue asymptotics and, as a by-product, sharp estimates of the splitting between two consecutive eigenvalues, for the Dirichlet magnetic Laplacian with a non-uniform magnetic field having a jump discontinuity along a smooth curve. The asymptotics hold in the semiclassical limit which also corresponds to a large magnetic field limit, and is valid under a geometric assumption on the curvature of the discontinuity curve.
34 pages