Hearing the shape of a magnetic edge in the semiclassical limit

Wafaa Assaad, Bernard Helffer, Ayman Kachmar

Published 2021-08-09Version 1

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.