The Dry Ten Martini Problem for $C^2$ cosine-type quasiperiodic Schr\"odinger operators
Mathematical Physics
2025-03-11 v1 Dynamical Systems
math.MP
Abstract
This paper solves ``The Dry Ten Martini Problem'' for cosine-type quasiperiodic Schr\"odinger operators with large coupling constants and Diophantine frequencies, a model originally introduced by Sinai in 1987 \cite{sinai}. This shows that the analyticity assumption on the potential is not essential for obtaining a dry Cantor spectrum and can be replaced by a certain geometric condition in the low regularity case. In addition, we prove the homogeneity of the spectrum and the absolute continuity of the integrated density of states (IDS).
Keywords
Cite
@article{arxiv.2503.06918,
title = {The Dry Ten Martini Problem for $C^2$ cosine-type quasiperiodic Schr\"odinger operators},
author = {Lingrui Ge and Yiqian Wang and Jiahao Xu},
journal= {arXiv preprint arXiv:2503.06918},
year = {2025}
}