Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$

Hongyi Cao; Shengquan Xiang

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arXiv · 2505.02339

Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$

Hongyi Cao·Shengquan Xiang

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Abstract

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 Schr\"odinger 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)).

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BibTeX RIS

Hongyi Cao, Shengquan Xiang. 2025-05-05. Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$. https://arxiv.org/abs/2505.02339

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