Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918009033981952 |
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| author | Cao, Hongyi Xiang, Shengquan |
| author_facet | Cao, Hongyi Xiang, Shengquan |
| contents | In this paper, we prove quantum ergodicity (a form of delocalization for eigenfunctions) for the Dirichlet truncations of the adjacency matrix on $\mathbb{Z}^d$. We also extend the result to the cases of finite range observables and periodic Schrödinger operators with periods of length at most two. This work partially answers a question asked by McKenzie and Sabri (Comm. Math. Phys. 403(3), 1477--1509(2023)). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02339 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$ Cao, Hongyi Xiang, Shengquan Spectral Theory Mathematical Physics In this paper, we prove quantum ergodicity (a form of delocalization for eigenfunctions) for the Dirichlet truncations of the adjacency matrix on $\mathbb{Z}^d$. We also extend the result to the cases of finite range observables and periodic Schrödinger operators with periods of length at most two. This work partially answers a question asked by McKenzie and Sabri (Comm. Math. Phys. 403(3), 1477--1509(2023)). |
| title | Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$ |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2505.02339 |