WKB constructions in bidimensional magnetic wells

Yannick Bonthonneau (1, 2) , Nicolas Raymond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Mathématiques [math]

Yannick Bonthonneau, Nicolas Raymond. WKB constructions in bidimensional magnetic wells. Mathematical Research Letters, 2020, 27 (3), pp.647 - 663. ⟨10.4310/MRL.2020.v27.n3.a2⟩. ⟨hal-01633638⟩