English

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}
}