English

Purely magnetic tunneling effect in two dimensions

Spectral Theory 2021-03-10 v2 Analysis of PDEs

Abstract

The semiclassical magnetic Neumann Schr\"odinger operator on a smooth, bounded, and simply connected domain Ω\Omega of the Euclidean plane is considered. When Ω\Omega 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.

Keywords

Cite

@article{arxiv.1912.04035,
  title  = {Purely magnetic tunneling effect in two dimensions},
  author = {Virginie Bonnaillie-Noël and Frédéric Hérau and Nicolas Raymond},
  journal= {arXiv preprint arXiv:1912.04035},
  year   = {2021}
}
R2 v1 2026-06-23T12:39:59.035Z