Tunneling effect in two dimensions with vanishing magnetic fields
Mathematical Physics
2022-12-09 v1 math.MP
Spectral Theory
Quantum Physics
Abstract
In this paper, we consider the semiclassical 2D magnetic Schr{\"o}dinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve has an axis of symmetry, we prove that semi-classical tunneling occurs. The main result is an expression the splitting of the first two eigenvalues and an explicit tunneling formula.
Keywords
Cite
@article{arxiv.2212.04289,
title = {Tunneling effect in two dimensions with vanishing magnetic fields},
author = {Khaled Abou Alfa},
journal= {arXiv preprint arXiv:2212.04289},
year = {2022}
}