The Schrödinger operator on an infinite wedge with a tangent magnetic field

Nicolas Popoff (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study a model Schrödinger operator with constant magnetic field on an infinite wedge with Neumann boundary condition. The magnetic field is assumed to be tangent to a face. We compare the bottom of the spectrum to the model spectral quantities coming from the regular case. We are particularly motivated by the influence of the magnetic field and the opening angle of the wedge on the spectrum of the model operator and we exhibit cases where the bottom of the spectrum is smaller than in the regular case. Numerical computations enlighten the theoretical approach.

Mots clés: Linear eigenvalue problem; Magnetic Schrödinger operator; Singular domain

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]

Nicolas Popoff. The Schrödinger operator on an infinite wedge with a tangent magnetic field. Journal of Mathematical Physics, 2013, 54 (4), 16 p. ⟨10.1063/1.4801784⟩. ⟨hal-00769450v3⟩