Sub-exponential localization for a random tight-binding model with long-range hopping

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-03-20 DOI:10.1016/j.jde.2025.113239

Siqi Xu , Dongfeng Yan

引用次数: 0

Abstract

In this paper, we study the Anderson tight-binding model on

Z^{d}

with the sub-exponential long-range hopping and log-Hölder continuously distributed potential. It is proved that, at high disorder this model has pure point spectrum with sub-exponentially decaying eigenfunctions. This gives a partial answer to a conjecture of Yeung-Oono [Europhys. Lett. 4(9), (1987): 1061-1065]. Our proof is based on multi-scale analysis type Green's function estimates.

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具有远程跳变的随机紧密结合模型的次指数定位

本文研究了具有次指数长程跳变和log-Hölder连续分布势的Zd上的Anderson紧密结合模型。证明了在高无序状态下，该模型具有具有亚指数衰减特征函数的纯点谱。这部分地回答了欧罗巴的一个猜想。生态学报，（1987）：1061-1065。我们的证明是基于多尺度分析型格林函数估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics