Purely magnetic tunneling effect in two dimensions

Virginie Bonnaillie-Noël (1) , Frédéric Hérau (2) , Nicolas Raymond (3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

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.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Théorie spectrale [math.SP]

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⟩