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Purely magnetic tunneling effect in two dimensions

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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https://hal.archives-ouvertes.fr/hal-02399073
Contributor : Nicolas Raymond Connect in order to contact the contributor
Submitted on : Tuesday, March 9, 2021 - 6:34:42 PM
Last modification on : Wednesday, April 27, 2022 - 3:59:34 AM

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  • HAL Id : hal-02399073, version 2

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Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond. Purely magnetic tunneling effect in two dimensions. Inventiones Mathematicae, Springer Verlag, In press. ⟨hal-02399073v2⟩

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