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Anderson localization for the multi-frequency quasi-periodic CMV matrices and quantum walks

2025/02/21 by Zhang, Bei, Piao, Daxiong
#37A30 #42C05 #70G60 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2502.15284

Abstract

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.

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