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Localization of the discrete one-dimensional quasi-periodic Schrödinger operators
  • Walid REFAI
Walid REFAI
Jazan University College of Science

Corresponding Author:wrefai@jazanu.edu.sa

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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.
14 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
14 Aug 2023Submission Checks Completed
14 Aug 2023Assigned to Editor
23 Aug 2023Review(s) Completed, Editorial Evaluation Pending
23 Aug 2023Reviewer(s) Assigned
10 Mar 20241st Revision Received
11 Mar 2024Submission Checks Completed
11 Mar 2024Assigned to Editor
11 Mar 2024Review(s) Completed, Editorial Evaluation Pending