Anderson localization for quasi-periodic CMV matrices and quantum walks
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2019
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Elsevier
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 Schrödinger operators. We also prove a similar result for quantum walks on the integer lattice with suitable analytic quasi-periodic coins.
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Wang, Fengpeng and Damanik, David. "Anderson localization for quasi-periodic CMV matrices and quantum walks." Journal of Functional Analysis, 276, no. 6 (2019) Elsevier: 1978-2006. https://doi.org/10.1016/j.jfa.2018.10.016.
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This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier.