Anderson Localization for Quasi-Periodic CMV Matrices and Quantum Walks
Spectral Theory
2019-02-25 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1804.00301,
title = {Anderson Localization for Quasi-Periodic CMV Matrices and Quantum Walks},
author = {Fengpeng Wang and David Damanik},
journal= {arXiv preprint arXiv:1804.00301},
year = {2019}
}
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22 pages