Green's function estimates for quasi-periodic operators on $\mathbb{Z}^d$ with power-law long-range hopping
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915600641556480 |
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| author | Shi, Yunfeng Wen, Li |
| author_facet | Shi, Yunfeng Wen, Li |
| contents | We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with power-law long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic version of localization, the finite volume version of $(\frac12-)$-Hölder continuity of the IDS, and the absence of eigenvalues (for Aubry dual operators). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01913 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Green's function estimates for quasi-periodic operators on $\mathbb{Z}^d$ with power-law long-range hopping Shi, Yunfeng Wen, Li Mathematical Physics Dynamical Systems Spectral Theory We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with power-law long-range hopping and analytic cosine type potentials. As applications, we prove the arithmetic version of localization, the finite volume version of $(\frac12-)$-Hölder continuity of the IDS, and the absence of eigenvalues (for Aubry dual operators). |
| title | Green's function estimates for quasi-periodic operators on $\mathbb{Z}^d$ with power-law long-range hopping |
| topic | Mathematical Physics Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2408.01913 |