Propagation of Semiclassical Measures Between Two Topological Insulators

TL;DR

This paper investigates how semiclassical measures evolve at the interface of two topological insulators with a Dirac operator model, using a two-scale Wigner measure approach to understand wave propagation in this complex system.

Contribution

It introduces a novel analysis of semiclassical measure propagation in a two-topological-insulator system with a non-compact interface, employing a two-scale Wigner measure method after Hamiltonian reduction.

Findings

Derived the evolution law for semiclassical measures at the interface.

Reduced the Hamiltonian to a normal form for analysis.

Provided insights into wave dynamics in topological insulator interfaces.

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.