Localization for Lipschitz monotone quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ via Rellich functions analysis
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929736955985920 |
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| author | Cao, Hongyi Shi, Yunfeng Zhang, Zhifei |
| author_facet | Cao, Hongyi Shi, Yunfeng Zhang, Zhifei |
| contents | We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on Rellich function analysis in the perturbative regime. We show that at each scale, the resonant Rellich function uniformly inherits the Lipschitz monotonicity property of the potential via a novel Schur complement argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01970 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localization for Lipschitz monotone quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ via Rellich functions analysis Cao, Hongyi Shi, Yunfeng Zhang, Zhifei Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on Rellich function analysis in the perturbative regime. We show that at each scale, the resonant Rellich function uniformly inherits the Lipschitz monotonicity property of the potential via a novel Schur complement argument. |
| title | Localization for Lipschitz monotone quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ via Rellich functions analysis |
| topic | Mathematical Physics Analysis of PDEs Dynamical Systems Spectral Theory |
| url | https://arxiv.org/abs/2407.01970 |