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 of the Euclidean plane is considered. When 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}
}