Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift
Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift
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DOI：
10.1016/j.jfa.2023.109975
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发表时间：
2022-09
影响因子：
1.7
通讯作者：
Yanxue Lin;Da-xiong Piao;Shuzheng Guo
中科院分区：
文献类型：
--
作者：
Yanxue Lin;Da-xiong Piao;Shuzheng Guo
本文研究了Verblunsky系数由斜移给出的拟周期CMV矩阵。我们证明了在几乎所有频率和大耦合参数下，系统的李雅普诺夫指数和安德森局部化均为正，从而建立了Bourgain等人[7]关于一维薛定谔算子的类似结果.
In this paper, we study quasi-periodic CMV matrices with Verblunsky coefficients given by the skew-shift. We prove the positivity of Lyapunov exponents and Anderson localization for almost all frequencies and large coupling parameter, which establish the analogous results of one-dimensional Schrödinger operators proved by Bourgain et al. [7].