Browsing by Author "Wang, Fengpeng"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Anderson localization for quasi-periodic CMV matrices and quantum walks
    (Elsevier, 2019) Wang, Fengpeng; Damanik, David
    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.
  • Thumbnail Image
    Item
    Positive Lyapunov exponents and a Large Deviation Theorem for continuum Anderson models, briefly
    (Elsevier, 2019) Bucaj, Valmir; Damanik, David; Fillman, Jake; Gerbuz, Vitaly; VandenBoom, Tom; Wang, Fengpeng; Zhang, Zhenghe
    In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to Damanik–Sims–Stolz, and it covers a wider variety of random models. Along the way we note that a Large Deviation Theorem holds uniformly on compacts.