Breaking a magnetic zero locus: model operators and numerical approach

Virginie Bonnaillie-Noël (1) , Nicolas Raymond (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 IRMAR - Institut de Recherche Mathématique de Rennes

This paper is devoted to the spectral analysis of a Schrödinger operator in presence of a vanishing magnetic field. The influence of the smoothness of the magnetic zeros locus is studied. In particular, it is proved that breaking the magnetic zero locus induces discrete spectrum below the essential spectrum. Numerical simulations illustrate the theoretical results.

Mots clés: singular zero locus; spectrum; magnetic; Schrödinger operator

Domaines: Equations aux dérivées partielles [math.AP]

Virginie Bonnaillie-Noël, Nicolas Raymond. Breaking a magnetic zero locus: model operators and numerical approach. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2015, 95 (2), pp.120-139. ⟨10.1002/zamm.201300086⟩. ⟨hal-00801365v3⟩