HOMOGENEOUS SPECTRUM OF QUASI-PERIODIC GEVREY SCHRODINGER OPERATORS WITH DIOPHANTINE FREQUENCY

被引：2

作者：

Yang, Yan ^{[1
]}

Tao, Kai ^{[1
]}

机构：

[1] Hohai Univ, Coll Sci, 1 Xikang Rd, Nanjing 210098, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年

关键词：

Homogeneous spectrum; Gevrey potential; Diophantine frequency; quasi-periodic Schr?dinger operator; large coupling number; DENSITY-OF-STATES; ANDERSON LOCALIZATION; HOLDER CONTINUITY; GAPS;

D O I：

10.3934/dcds.2022166

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the quasi-periodic Schrodinger operator with the non-degenerate Gevrey potential for the Diophantine frequency. We prove that if the coupling constant of the potential is large enough, then the spectrum is homogeneous.

引用

页码：688 / 714

页数：27

共 50 条

[41] Quasi-periodic solutions with prescribed frequency in a nonlinear Schrodinger equation
Ren Xiu-Fang
SCIENCE CHINA-MATHEMATICS, 2010, 53 (12) : 3067 - 3084
[42] Quasi-periodic solutions of two dimensional SchrOdinger equations with Quasi-periodic forcing'
Zhang, Min
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 135 : 1 - 34
[43] GLOBAL SCALING PROPERTIES OF THE SPECTRUM FOR A QUASI-PERIODIC SCHRODINGER-EQUATION
TANG, C
KOHMOTO, M
PHYSICAL REVIEW B, 1986, 34 (03): : 2041 - 2044
[44] Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation
Yunfeng Shi
Journal d'Analyse Mathématique, 2022, 148 : 305 - 338
[45] Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation
Shi, Yunfeng
JOURNAL D ANALYSE MATHEMATIQUE, 2022, 148 (01): : 305 - 338
[46] Anderson localization for quasi-periodic lattice schrodinger operators on zd, d arbitrary
Bourgain, Jean
GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (03) : 682 - 706
[47] Upper bounds on the spectral gaps of quasi-periodic Schrodinger operators with Lionville frequencies
Liu, Wencai
Shi, Yunfeng
JOURNAL OF SPECTRAL THEORY, 2019, 9 (04) : 1223 - 1248
[48] Dispersive estimate for quasi-periodic Schrodinger operators on 1-d lattices
Bambusi, Dario
Zhao, Zhiyan
ADVANCES IN MATHEMATICS, 2020, 366
[49] Anderson localization for Schrodinger operators on Z2 with quasi-periodic potential
Bourgain, J
Goldstein, M
Schlag, W
ACTA MATHEMATICA, 2002, 188 (01) : 41 - 86
[50] Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators
Cao, Hongyi
Shi, Yunfeng
Zhang, Zhifei
SCIENCE CHINA-MATHEMATICS, 2024, 67 (05) : 1011 - 1058

← 1 2 3 4 5 →