On the AC spectrum of one-dimensional random Schrödinger operators with matrix-valued potentials
type: Item
instance of: scholarly article
title: On the AC spectrum of one-dimensional random Schrödinger operators with matrix-valued potentials
zbMATH Open document ID: 1257.82058
author: Richard Froese
author: David Hasler
author: Wolfgang Spitzer
published in: Mathematical Physics, Analysis and Geometry
publication date: 2012-06-20T00:00:00Z
full work available at URL: https://arxiv.org/abs/0912.0294
review text: The authors are interested in the absolutely continuous spectrum of discrete one-dimensional random Schrödinger operators with decaying potentials. The problem is formulated in terms of matrix-valued independent potentials on the one-dimensional lattice \(\mathbb{Z}\). If the \(\ell^2\)-norm of the underlying potential has finite expectation value with respect to the product measure, then almost surely the Schrödinger operator has an interval of purely absolutely continuous spectrum, depending on the constant `potential' part of the Schrödinger operator. The proof is based on a study of the corresponding Green functions. The obtained result is applied to Schrödinger operators on a strip. This work provides a new proof and generalizes a result obtained by \textit{F. Delyon, B. Simon} and \textit{B. Souillard} [Ann. Inst. Henri Poincaré, Phys. Théor. 42, 283--309 (1985; Zbl 0579.60056)].
reviewed by: Martin Grothaus
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 62M15
zbMATH DE Number: 6048552
zbMATH Keywords: random Schrödinger operators
zbMATH Keywords: spectral analysis
MaRDI profile type: Publication
OpenAlex ID: W3101579701
arXiv ID: 0912.0294
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DOI: 10.1007/S11040-010-9076-9
description: scientific article; zbMATH DE number 6048552