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Journal Articles Inventiones Mathematicae Year : 2021

Purely magnetic tunneling effect in two dimensions


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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Dates and versions

hal-02399073 , version 1 (08-12-2019)
hal-02399073 , version 2 (09-03-2021)



Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond. Purely magnetic tunneling effect in two dimensions. Inventiones Mathematicae, In press, ⟨10.1007/s00222-021-01073-x⟩. ⟨hal-02399073v2⟩
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