{"title":"Sub-exponential localization for a random tight-binding model with long-range hopping","authors":"Siqi Xu , Dongfeng Yan","doi":"10.1016/j.jde.2025.113239","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study the Anderson tight-binding model on <span><math><msup><mrow><mi>Z</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> 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 [<em>Europhys. Lett.</em> 4(9), (1987): 1061-1065]. Our proof is based on multi-scale analysis type Green's function estimates.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"431 ","pages":"Article 113239"},"PeriodicalIF":2.3000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625002542","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the Anderson tight-binding model on 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.
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
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
