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arXiv · 1804.00301

Anderson Localization for Quasi-Periodic CMV Matrices and Quantum Walks

Fengpeng Wang·David Damanik
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Abstract

We consider CMV matrices, both standard and extended, with analytic quasi-periodic Verblunsky coefficients and prove Anderson localization in the regime of positive Lyapunov exponents. This establishes the CMV analog of a result Bourgain and Goldstein proved for discrete one-dimensional Schr\"odinger operators. We also prove a similar result for quantum walks on the integer lattice with suitable analytic quasi-periodic coins.

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Fengpeng Wang, David Damanik. 2018-04-01. Anderson Localization for Quasi-Periodic CMV Matrices and Quantum Walks. https://arxiv.org/abs/1804.00301

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