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Autori principali: Ge, Lingrui, Wang, Yiqian, Xu, Jiahao
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2503.06918
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author Ge, Lingrui
Wang, Yiqian
Xu, Jiahao
author_facet Ge, Lingrui
Wang, Yiqian
Xu, Jiahao
contents This paper solves ``The Dry Ten Martini Problem'' for $C^2$ cosine-type quasiperiodic Schrödinger 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).
format Preprint
id arxiv_https___arxiv_org_abs_2503_06918
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Dry Ten Martini Problem for $C^2$ cosine-type quasiperiodic Schrödinger operators
Ge, Lingrui
Wang, Yiqian
Xu, Jiahao
Mathematical Physics
Dynamical Systems
37C05
This paper solves ``The Dry Ten Martini Problem'' for $C^2$ cosine-type quasiperiodic Schrödinger 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).
title The Dry Ten Martini Problem for $C^2$ cosine-type quasiperiodic Schrödinger operators
topic Mathematical Physics
Dynamical Systems
37C05
url https://arxiv.org/abs/2503.06918