Remark on the absence of absolutely continuous spectrum for d-dimensional Schrödinger operators with random potential for large disorder or low energy
type: Item
instance of: scholarly article
title: Remark on the absence of absolutely continuous spectrum for d-dimensional Schrödinger operators with random potential for large disorder or low energy
zbMATH Open document ID: 0603.60060
DOI: 10.1007/BF01213410
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: We show that there is no absolutely continuous part in the spectrum of the Anderson tight-binding model for large disorder or low energy. The proof is based on the exponential decay of the Green's function proved by \textit{J. Fröhlich} and \textit{T. Spencer} [Commun. Math. Phys. 88, 151-184 (1983; Zbl 0519.60066)]. The extension of this result to the continuous case is also discussed.
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 81P20
zbMATH DE Number: 3973989
zbMATH Keywords: Schrödinger operators
zbMATH Keywords: Anderson tight-binding model
zbMATH Keywords: Green's function
author: Fabio Martinelli
author: E. Scoppola
MaRDI profile type: Publication
cites work: Spectral properties of disordered systems in the one-body approximation
cites work: Sur le spectre des opérateurs aux différences finies aléatoires
cites work: Absence of diffusion in the Anderson tight binding model for large disorder or low energy
cites work: Schrödinger semigroups
cites work: Q3932078
cites work: On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator on \(L^ 2({\mathbb{R}}^ v)^+\)
full work available at URL: https://doi.org/10.1007/bf01213410
OpenAlex ID: W1979299247
description: scientific article; zbMATH DE number 3973989