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

共 50 条

[1] Resonance Tongues and Spectral Gaps in Quasi-Periodic Schrodinger Operators with One or More Frequencies. A Numerical Exploration
Puig, Joaquim
Simo, Carles
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2011, 23 (03) : 649 - 669
[2] On the formation of gaps in the spectrum of schrodinger operators with quasi-periodic potentials
Goldstein, Michael
Schlag, Wilhelm
Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday: ERGODIC SCHRODINGER OPERATORS, SINGULAR SPECTRUM, ORTHOGONAL POLYNOMIALS, AND INVERSE SPECTRAL THEORY, 2007, 76 : 591 - 611
[3] On quasi-periodic lattice Schrodinger operators
Bourgain, J
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2004, 10 (1-2) : 75 - 88
[4] Dynamics and spectral theory of quasi-periodic Schrodinger-type operators
Marx, C. A.
Jitomirskaya, S.
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2017, 37 : 2353 - 2393
[5] Homogeneity of the spectrum for quasi-periodic Schrodinger operators
Damanik, David
Goldstein, Michael
Schlag, Wilhelm
Voda, Mircea
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2018, 20 (12) : 3073 - 3111
[6] Cantor spectrum for quasi-periodic Schrodinger operators
Puig, Joaquirn
Mathematical Physics of Quantum Mechanics: SELECTED AND REFEREED LECTURES FROM QMATH9, 2006, 690 : 79 - 91
[7] Holder Continuity of Spectral Measures for the Finitely Differentiable Quasi-Periodic Schrodinger Operators
Sun, Mei
Wang, Xueyin
ANALYSIS IN THEORY AND APPLICATIONS, 2020, 36 (01) : 33 - 51
[8] Holder Continuity of Spectral Measures for the Finitely Differentiable Quasi-Periodic Schrodinger Operators
Mei Sun
Xueyin Wang
AnalysisinTheoryandApplications, 2020, 36 (01) : 33 - 51
[9] Extremal spectral gaps for periodic Schrodinger operators
Kao, Chiu-Yen
Osting, Braxton
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[10] Resonance Tongues and Spectral Gaps in Quasi-Periodic Schrödinger Operators with One or More Frequencies. A Numerical Exploration
Joaquim Puig
Carles Simó
Journal of Dynamics and Differential Equations, 2011, 23 : 649 - 669

← 1 2 3 4 5 →