Magnetic WKB constructions on surfaces
Spectral Theory
2021-03-16 v1 Mathematical Physics
math.MP
Abstract
This article is devoted to the description of the eigenvalues and eigenfunctions of the magnetic Laplacian in the semiclassical limit via the complex WKB method. Under the assumption that the magnetic field has a unique and non-degenerate minimum, we construct the local complex WKB approximations for eigenfunctions on a general surface. Furthermore, in the case of the Euclidean plane, with a radially symmetric magnetic field, the eigenfunctions are approximated in an exponentially weighted space.
Keywords
Cite
@article{arxiv.2003.00985,
title = {Magnetic WKB constructions on surfaces},
author = {Yannick Guedes Bonthonneau and Tho Nguyen Duc and Nicolas Raymond and San Vũ Ngoc},
journal= {arXiv preprint arXiv:2003.00985},
year = {2021}
}
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31 pages