The Dry Ten Martini Problem for Sturmian Hamiltonians
Mathematical Physics
2024-02-27 v1 math.MP
Spectral Theory
Abstract
The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics.
Keywords
Cite
@article{arxiv.2402.16703,
title = {The Dry Ten Martini Problem for Sturmian Hamiltonians},
author = {Ram Band and Siegfried Beckus and Raphael Loewy},
journal= {arXiv preprint arXiv:2402.16703},
year = {2024}
}