On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations

2016/04/28 by Vanderléa R. Bazao, Bazao, Vanderlea R., Silas L. Carvalho +3
Mathematics · Physics and Astronomy · #47B36 #81Q35 #82B41 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · doi:10.48550/arxiv.1604.08542

openalex publication_date 2016/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that spectral Hausdorff dimensional properties of discrete Schröodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.

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