Localization of the discrete one‐dimensional quasi‐periodic Schrödinger operators

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 large disorder, under some suitable conditions on and a diophantine rotation number, we prove using basically KAM theory that the spectrum of this operator is pure point for all with exponential decaying eigenfunctions.