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Main Authors: Zhang, Bei, Piao, Daxiong
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2502.15284
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author Zhang, Bei
Piao, Daxiong
author_facet Zhang, Bei
Piao, Daxiong
contents In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov exponents. By constructing a suitable semialgebraic set and combining the Avalanche Principle with a Large Deviation Theorem, we overcome the key obstruction of eliminating double resonances along the orbit, where multi-frequency potentials introduce significant challenges compared to the single-frequency case. As a direct application, we establish Anderson localization for corresponding analytic multi-frequency quasi-periodic quantum walks via unitary equivalence.
format Preprint
id arxiv_https___arxiv_org_abs_2502_15284
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks
Zhang, Bei
Piao, Daxiong
Spectral Theory
37A30, 42C05, 70G60
In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov exponents. By constructing a suitable semialgebraic set and combining the Avalanche Principle with a Large Deviation Theorem, we overcome the key obstruction of eliminating double resonances along the orbit, where multi-frequency potentials introduce significant challenges compared to the single-frequency case. As a direct application, we establish Anderson localization for corresponding analytic multi-frequency quasi-periodic quantum walks via unitary equivalence.
title Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks
topic Spectral Theory
37A30, 42C05, 70G60
url https://arxiv.org/abs/2502.15284