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

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 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)).