Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$
Spectral Theory
2025-05-06 v1 Mathematical Physics
math.MP
Abstract
In this paper, we prove quantum ergodicity (a form of delocalization for eigenfunctions) for the Dirichlet truncations of the adjacency matrix on . 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)).
Cite
@article{arxiv.2505.02339,
title = {Quantum ergodicity for Dirichlet-truncated operators on $\mathbb{Z}^d$},
author = {Hongyi Cao and Shengquan Xiang},
journal= {arXiv preprint arXiv:2505.02339},
year = {2025}
}