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arXiv · 1912.04035

Purely magnetic tunneling effect in two dimensions

Virginie Bonnaillie-Noël·Frédéric Hérau·Nicolas Raymond
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Abstract

The semiclassical magnetic Neumann Schrödinger operator on a smooth, bounded, and simply connected domain $Ω$ of the Euclidean plane is considered. When $Ω$ has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic Agmon estimates.

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Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond. 2021-03-09. Purely magnetic tunneling effect in two dimensions. https://arxiv.org/abs/1912.04035

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