Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909287204257792 |
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| author | Rangamani, Nishant Zhu, Xiaowen |
| author_facet | Rangamani, Nishant Zhu, Xiaowen |
| contents | We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the $\mathbb{Z}^2$ and $\mathbb{Z}^3$ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01608 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$ Rangamani, Nishant Zhu, Xiaowen Mathematical Physics Spectral Theory We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical localization (SDL). In particular, given the recent progress at the bottom of the spectrum for the $\mathbb{Z}^2$ and $\mathbb{Z}^3$ cases with Bernoulli single site probability distribution, our results imply SDL in these regimes. |
| title | Dynamical Localization for the Singular Anderson Model in $\mathbb{Z}^d$ |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2307.01608 |