Edge State Propagation Near Multiple and Singular Interfaces

We study the semi-classical propagation of edge-states for a two-dimensional Dirac operator with a spatially varying mass. The zero set of the mass models the interface between topological phases and is allowed either to consist of two disjoint smooth curves or to possess an isolated singular point. For disjoint interfaces, we prove that a wave packet initially localized on one component remains confined near this interface over long semiclassical time scales and we quantify the influence of the distance between the two components on the accuracy of the approximation. For singular interfaces, we determine the regime in which the wave-packet approximation remains valid as the packet approaches the singularity and identify the scaling at which our estimates lose their uniformity.