Absolutely continuous spectrum of perturbed Stark operators

1997/03/05 by Alexander Kiselev, Kiselev, Alexander
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/9703205

openalex publication_date 1997/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark operator is stable if the perturbing potential decays at the rate (1+x)^-(1)/(3)-ε or if it is continuously differentiable with derivative from the Hölder space C_α(R), with any α>0.

Citations

• Preservation of the absolutely continuous spectrum of Schrödinger equation under perturbations by slowly decreasing potentials and a.e. convergence of integral operators

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