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Walid REFAI
Walid REFAI

Public Documents 1
Localization of the discrete one-dimensional quasi-periodic Schrödinger operators
Walid REFAI

Walid REFAI

August 14, 2023
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.

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