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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2503.06918 |
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| _version_ | 1866915189628076032 |
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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 |