On the spectrum of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with $C^2$-cosine type potentials
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866911912203124736 |
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| author | Cao, Hongyi Shi, Yunfeng Zhang, Zhifei |
| author_facet | Cao, Hongyi Shi, Yunfeng Zhang, Zhifei |
| contents | In this paper, we establish the Anderson localization, strong dynamical localization and the $(\frac 12-)$-Hölder continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schrödinger operators with asymmetric $C^2$-cosine type potentials. We extend both the iteration scheme of \cite{CSZ23a} and the interlacing method of \cite{FV21} to handle asymmetric Rellich functions with collapsed gaps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07407 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the spectrum of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with $C^2$-cosine type potentials Cao, Hongyi Shi, Yunfeng Zhang, Zhifei Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory In this paper, we establish the Anderson localization, strong dynamical localization and the $(\frac 12-)$-Hölder continuity of the integrated density of states (IDS) for some multi-dimensional discrete quasi-periodic (QP) Schrödinger operators with asymmetric $C^2$-cosine type potentials. We extend both the iteration scheme of \cite{CSZ23a} and the interlacing method of \cite{FV21} to handle asymmetric Rellich functions with collapsed gaps. |
| title | On the spectrum of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with $C^2$-cosine type potentials |
| topic | Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2310.07407 |