Directional Ballistic Transport in Quantum Waveguides
Spectral Theory
2026-01-21 v1 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We study the transport properties of Schr\"odinger operators on with potentials that are periodic in some directions and compactly supported in the others. Such systems are known to produce surface states that are weakly confined near the support of the potential. We show that a natural set of surface states exhibits directional ballistic transport, characterized by ballistic transport in the periodic directions and its absence in the others. To prove this, we develop a Floquet theory that captures the analytic variation of surface states. The main idea consists of reformulating the eigenvalue problem for surface states as a Fredholm problem via the Dirichlet-to-Neumann map.
Keywords
Cite
@article{arxiv.2601.13471,
title = {Directional Ballistic Transport in Quantum Waveguides},
author = {Adam Black and David Damanik and Peter Kuchment and Tal Malinovitch and Giorgio Young},
journal= {arXiv preprint arXiv:2601.13471},
year = {2026}
}