We consider a Dirac system confined to a domain $\Omega$ in the plane and subject to a perpendicular magnetic field. In this talk I will present results on accurate asymptotic estimates for the low-lying eigen-energies in the limit of strong magnetic field under fairly general local boundary conditions. We will focus on the case of infinite mass boundary conditions. In particular, we will see the emergence of exceptional energies, very stable in the geometry, which can be heuristically understood by looking at the half-plane problem.

This talk is based on joint work with Jean-Marie Barbaroux (Université de Toulon), Loic Le Treust (Aix Marseille Univ, France) and Nicolas Raymond (Université d’Angers); arXiv: 1810.03344 (JEMS '21) and arXiv: 2007.03242.

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