Quantum diffusion and delocalization in one-dimensional band matrices via the flow method
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916534285238272 |
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| author | Dubova, Sofiia Yang, Kevin |
| author_facet | Dubova, Sofiia Yang, Kevin |
| contents | We study a class of Gaussian random band matrices of dimension $N \times N$ and band-width $W$. We show that delocalization holds for bulk eigenvectors and that quantum diffusion holds for the resolvent, all under the assumption that $W \gg N^{8/11}$. Our analysis is based on a flow method, and a refinement of it may lead to an improvement on the condition $W \gg N^{8/11}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum diffusion and delocalization in one-dimensional band matrices via the flow method Dubova, Sofiia Yang, Kevin Probability Mathematical Physics 60B20, 82B44 We study a class of Gaussian random band matrices of dimension $N \times N$ and band-width $W$. We show that delocalization holds for bulk eigenvectors and that quantum diffusion holds for the resolvent, all under the assumption that $W \gg N^{8/11}$. Our analysis is based on a flow method, and a refinement of it may lead to an improvement on the condition $W \gg N^{8/11}$. |
| title | Quantum diffusion and delocalization in one-dimensional band matrices via the flow method |
| topic | Probability Mathematical Physics 60B20, 82B44 |
| url | https://arxiv.org/abs/2412.15207 |