Author(s)

Walid Refai

Department of Mathematics, College of Addair, Jazan University, Jizan, Saudi Arabia.

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).

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

Refai, W. (2023) Dynamical Localization of the Quasi-Periodic Schrödinger Operators. Open Access Library Journal, 10, 1-13. doi: 10.4236/oalib.1110966.