Propagation of Semiclassical Measures Between Two Topological Insulators

Abstract

We study propagation in a system consisting of two topological insulators without a magnetic field, whose interface is a non-compact, smooth, and connected curve without boundary. The dynamics are governed by an adiabatic modulation of a Dirac operator with a smooth, effective variable mass. We determine the evolution of the semiclassical measure of the solution using a two-scale Wigner measure method, after reducing the Hamiltonian to a normal form.