Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (5): 1240-1254.doi: 10.1007/s10473-019-0504-z

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SHARP HÖLDER CONTINUITY OF THE INTEGRATED DENSITY OF STATES FOR EXTENDED HARPERS MODEL WITH A LIOUVILLE FREQUENCY

Wenwen JIAN1, Yunfeng SHI2   

  1. 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;
    2. School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2018-06-28 Revised:2018-10-27 Online:2019-10-25 Published:2019-11-11
  • Contact: Yunfeng SHI E-mail:yunfengshi18@gmail.com
  • Supported by:
    The second author was supported by China Postdoctoral Science Foundation (2018M641050).

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 1/2-Hölder continuous. As an application, the homogeneity of the spectrum is proven.

Key words: extended Harper's model, Liouville frequency, 1/2-Hölder continuity, homogeneity

CLC Number: 

  • 47B36
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