Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue
Bernard Helffer
Université de Nantes, FranceAyman Kachmar
The Chinese University of Hong Kong, China; Lebanese University, Nabatiyeh, Lebanon
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Abstract
We study the three-dimensional Neumann magnetic Laplacian in the presence of a semiclassical 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.
Cite this article
Bernard Helffer, Ayman Kachmar, Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue. Doc. Math. 28 (2023), no. 4, pp. 857–901
DOI 10.4171/DM/922