Magnetic Schrödinger and Dirac operators on a curved strip
Opérateurs magnétiques de Schrödinger et Dirac sur une bande courbée

13 – 17 December 2021

The aim of this mini-workshop is to explore the discrete spectrum of the magnetic Schrödinger and Dirac operators on a curved strip. These operators are equipped with the Dirichlet and infinite mass conditions, respectively. Since these operators are considered on a curved strip, the essential spectrum is non-empty. We wish to describe it, especially in the strong magnetic field regime. Once the essential spectrum is determined, a natural question appears: does the discrete spectrum exist? It is well-known that, when the strip is curved and without magnetic field, the discrete spectrum of the Dirichlet Laplacian exists. What happens when the magnetic field is turned on? Does the discrete spectrum survive? To answer these questions, one will use the strategies developped recently in our paper and try to extend them to unbounded domains.

Jean-Marie Barbaroux (Université de Toulon & CPT Marseille)
Enguerrand Lavigne-Bon (Aix-Marseille Université)
Loïc Le Treust (Aix-Marseille Université)

Nicolas Raymond (Université d’Angers)
Eric Soccorsi (Aix-Marseille Université)

This workshop is supported by the IRN project (CNRS) SPEDO.