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Sharp Hölder Continuity of the Integrated Density of States for Extended Harper’s Model with a Liouville Frequency

Authors
  • Jian, Wenwen1
  • Shi, Yunfeng2
  • 1 Fudan University, School of Mathematical Sciences, Shanghai, 200433, China , Shanghai (China)
  • 2 Peking University, School of Mathematical Sciences, Beijing, 100871, China , Beijing (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer Singapore
Publication Date
Jul 10, 2019
Volume
39
Issue
5
Pages
1240–1254
Identifiers
DOI: 10.1007/s10473-019-0504-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

In this article, the non-self dual extended Harper’s model with a Liouville frequency is considered. It is shown that the corresponding integrated density of states is 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document}-Hölder continuous. As an application, the homogeneity of the spectrum is proven.

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