Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue
Spectral Theory
2022-04-22 v1
Abstract
We study the 3D Neuman magnetic Laplacian in the presence of a semi-classical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asymptotics for the lowest eigenvalue, where the second term involves a quantity related to the magnetic field and the geometry of the domain. In the special case of the unit ball and a helical magnetic field, the concentration takes place on two symmetric points of the unit sphere.
Keywords
Cite
@article{arxiv.2204.09880,
title = {Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue},
author = {Bernard Helffer and Ayman Kachmar},
journal= {arXiv preprint arXiv:2204.09880},
year = {2022}
}