Edge states in ordinary differential equations for dislocations
Mathematical Physics
2020-05-20 v1 Classical Analysis and ODEs
math.MP
Abstract
In this article, we study Schr\"odinger operators on the real line, when the external potential represents a dislocation in a periodic medium. We study how the spectrum varies with the dislocation parameter. We introduce several integer-valued indices, including Chern number for bulk indices, and various spectral flows for edge indices. We prove that all these indices coincide, providing a proof a bulk-edge correspondence in this case. The study is also made for dislocations in Dirac models on the real line. We prove that 0 is always an eigenvalue of such operators.
Keywords
Cite
@article{arxiv.1908.01377,
title = {Edge states in ordinary differential equations for dislocations},
author = {David Gontier},
journal= {arXiv preprint arXiv:1908.01377},
year = {2020}
}