Spectral approximation for substitution systems
Abstract
Abstract We study periodic approximations of aperiodic Schrödinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems that have been recently introduced in this setting. We characterize convergence of spectra of associated Schrödinger operators in the Hausdorff distance via properties of finite graphs. As a consequence, new examples of periodic approximations are obtained. We further prove that there are substitution systems that do not admit periodic approximations in higher dimensions, in contrast to the one-dimensional case. On the other hand, if the spectra converge, then we show that the rate of convergence is necessarily exponentially fast. These results are new even for substitutions over ℤ d .
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Quantum chaos and dynamical systems
semigroups and automata theory
Publication details
- Journal / source
- Journal d Analyse Mathématique
- Publisher
- Springer Science and Business Media LLC
- Volume
- 159
- Issue
- 1
- Pages
- 267–312
- Publication date
- 19 April 2026
- Language
- EN