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
v and a diophantine rotation number, we prove using basically
K.A.M theory that the spectrum of this operator is pure point for all
θ∈[0 ,2 π) with exponential decaying
eigenfunctions.