Spectral pollution in substitution 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.