Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift

Yanxue Lin; Daxiong Piao; Shuzheng Guo

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arXiv · 2209.07012

Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift

Yanxue Lin·Daxiong Piao·Shuzheng Guo

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Abstract

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 most frequencies, which establish the analogous results of one-dimensional Schr\"{o}dinger operators proved by Bourgain, Goldstein and Schlag.

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Yanxue Lin, Daxiong Piao, Shuzheng Guo. 2022-09-15. Anderson localization for the quasi-periodic CMV matrices with Verblunsky coefficients defined by the skew-shift. https://arxiv.org/abs/2209.07012

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