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).