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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