Edge States for Generalized Iwatsuka Models: Magnetic Fields Having a Fast Transition Across a Curve

Abstract

In this paper, we study the localization and propagation properties of the edge states associated with a class of magnetic Laplacians in mathbb {R}^2. We assume that the intensity of the magnetic field has a fast transition along a regular and compact curve Gamma . Our main results extend to a general regular curve the study of the localized eigenfunction obtained when Gamma is a straight line (i.e. Iwatsuka models). Furthermore, we include in our analysis the case of magnetic fields that slowly change along the curve Gamma and we obtain a rigorous and explicit characterization of the asymptotic mass distribution of the edge state along Gamma .