Spectral pollution in substitution systems
Spectral Theory
2026-04-15 v1 Dynamical Systems
Abstract
We study spectral properties of Schr\"odinger operators associated with substitution dynamical systems in higher dimensions. Focusing on periodic approximations generated by iterating substitutions on initial configurations, we analyze how structural defects influence the limiting spectral behavior. In contrast to the one-dimensional setting, we show that such approximations may exhibit significant spectral pollution, including changes in the essential spectrum and the Lebesgue measure.
Cite
@article{arxiv.2604.12637,
title = {Spectral pollution in substitution systems},
author = {Ram Band and Siegfried Beckus and Felix Pogorzelski and Lior Tenenbaum},
journal= {arXiv preprint arXiv:2604.12637},
year = {2026}
}
Comments
There are very narrow spectral bands in Figure 2. These are better visible in PDF viewers than in browser-based viewers