Upper bounds on the spectral gaps of quasi-periodic Schrodinger operators with Lionville frequencies

被引：9

作者：

Liu, Wencai ^{[1
,2
]}

Shi, Yunfeng ^{[3
,4
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[4] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

JOURNAL OF SPECTRAL THEORY | 2019年 / 9卷 / 04期

关键词：

Quasi-periodic Schrodinger operators; spectral gaps; Liouville frequencies; upper bounds; HOLDER CONTINUITY; ROTATION NUMBER; REDUCIBILITY; LOCALIZATION; HOMOGENEITY;

D O I：

10.4171/JST/275

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schrodinger operators with Liouville frequencies decays exponentially. As an application, we obtain the homogeneity of the spectrum.

引用

页码：1223 / 1248

页数：26

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