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arXiv · 2108.03964

Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit)

Wafaa Assaad·Bernard Helffer·Ayman Kachmar
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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.

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Wafaa Assaad, Bernard Helffer, Ayman Kachmar. 2021-08-09. Semi-classical eigenvalue estimates under magnetic steps (Former title: Hearing the shape of a magnetic edge in the semiclassical limit). https://doi.org/10.2140/apde.2024.17.535

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