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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.

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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