On Duclos–Exner’s conjecture about waveguides in strong uniform magnetic fields

Abstract

We consider the Dirichlet Laplacian with uniform magnetic field on a curved strip in two dimensions. We give a sufficient condition on the width and the curvature of the strip ensuring the existence of the discrete spectrum in the strong magnetic field limit, answering (negatively) a conjecture made by Duclos and Exner.

Keywords

• 35P15
• 81Q10