Year: 2025
Type: article
Abstract: In this paper we study the spectral properties of a family of discrete one-dimensional quasi-periodic Schrödinger operators with discontinuous potential. In large disorder with piecewise analytic potential, under some suitable transversality condition and a Diophantine rotation number, we prove using basically KAM theory that the spectrum of this operator have a large punctual component. Moreover, the most of its eigenvectors are ℓ 2 -localized in one site. We give an explicit estimation of the measure of the punctual spectrum and we prove that the set of phases for which this spectrum is empty have zero Hausdorff dimension.
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.730
Author: Walid Refai
Institution: Jazan University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410524924