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Bourgain, J. and Goldstein, M. (2000) On Nonperturbative Localization with Quasi-Periodic Potential. Annals of Mathematics, 152, 835-879. https://doi.org/10.2307/2661356

has been cited by the following article:

• TITLE: Dynamical Localization of the Quasi-Periodic Schrödinger Operators

  AUTHORS: Walid Refai

  KEYWORDS: Quasi-Periodic Schrödinger Operators, Pure Point Spectrum, Eigenfunctions, Dynamical Localization

  JOURNAL NAME: Open Access Library Journal, Vol.10 No.12, December 29, 2023

  ABSTRACT: In this paper, we study the spectral properties of a family of discrete one-dimensional quasi-periodic Schrödinger operators (depending on a phase theta). In the perturbative regime and in large disorder, under some conditions on v and a diophantine rotation number, we prove by using KAM theory that this operator satisfies both Anderson and dynamical localization for all θ∈[0,2π).