Lyapunov behavior and dynamical localization for quasi-periodic CMV matrices

被引:1
作者
Guo, Shuzheng [1 ]
Piao, Daxiong [1 ]
机构
[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Peoples R China
关键词
CMV matrix; Anderson localization; Lyapunov behavior; Dynamical localization; Quasi-periodic coefficient; ORTHOGONAL POLYNOMIALS; HOLDER CONTINUITY; EXPONENTS; OPERATORS; POSITIVITY; ZEROS;
D O I
10.1016/j.laa.2020.07.031
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we prove Lyapunov behavior and dynamical localization for analytic quasi-periodic CMV matrices in the regime of positive Lyapunov exponents. The localization results of Wang and Damanik [28] are extended. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码:68 / 89
页数:22
相关论文
共 32 条
  • [1] ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES
    ANDERSON, PW
    [J]. PHYSICAL REVIEW, 1958, 109 (05): : 1492 - 1505
  • [2] Positive Lyapunov exponents for continuous quasiperiodic Schrodinger equations
    Bjerklöv, K
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (02)
  • [3] On nonperturbative localization with quasi-periodic potential
    Bourgain, J
    Goldstein, M
    [J]. ANNALS OF MATHEMATICS, 2000, 152 (03) : 835 - 879
  • [4] Positive Lyapunov exponents and a Large Deviation Theorem for continuum Anderson models, briefly
    Bucaj, Valmir
    Damanik, David
    Fillman, Jake
    Gerbuz, Vitaly
    VandenBoom, Tom
    Wang, Fengpeng
    Zhang, Zhenghe
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 277 (09) : 3179 - 3186
  • [5] LOCALIZATION FOR THE ONE-DIMENSIONAL ANDERSON MODEL VIA POSITIVITY AND LARGE DEVIATIONS FOR THE LYAPUNOV EXPONENT
    Bucaj, Valmir
    Damanik, David
    Fillman, Jake
    Gerbuz, Vitaly
    Vandenboom, Tom
    Wang, Fengpeng
    Zhang, Zhenghe
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (05) : 3619 - 3667
  • [6] Cantero MJ, 2010, COMMUN PUR APPL MATH, V63, P464
  • [7] Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle
    Cantero, MJ
    Moral, L
    Velázquez, L
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 362 : 29 - 56
  • [8] CHARACTERIZATIONS OF UNIFORM HYPERBOLICITY AND SPECTRA OF CMV MATRICES
    Damanik, David
    Fillman, Jake
    Lukic, Milivoje
    Yessen, William
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2016, 9 (04): : 1009 - 1023
  • [9] Spreading estimates for quantum walks on the integer lattice via power-law bounds on transfer matrices
    Damanik, David
    Fillman, Jake
    Ong, Darren C.
    [J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2016, 105 (03): : 293 - 341
  • [10] Davies EB, 2006, J APPROX THEORY, V141, P189, DOI 10.1016/j.jat.2006.03.006