WKB constructions in bidimensional magnetic wells
Yannick Bonthonneau, Nicolas Raymond
TL;DR
This paper develops WKB methods to construct eigenfunctions for the magnetic Laplacian in two dimensions, focusing on low-energy states near a unique, positive, and non-degenerate magnetic field minimum.
Contribution
It provides the first analytic WKB constructions for eigenfunctions of the magnetic Laplacian with a single minimum magnetic field in two dimensions.
Findings
WKB constructions for eigenfunctions near magnetic minima
Analysis of low-energy eigenstates in magnetic wells
First analytic approach in this setting
Abstract
This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy when the magnetic field has a unique minimum that is positive and non-degenerate.
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