Schrödinger operators with random sparse potentials. Existence of wave operators
type: Item
instance of: scholarly article
title: Schrödinger operators with random sparse potentials. Existence of wave operators
zbMATH Open document ID: 1066.47007
author: Denis Krutikov
published in: Letters in Mathematical Physics
publication date: 2004-08-16T00:00:00Z
review text: The existence of wave operators is proved for operator pairs of the form \(\{-\Delta,-\Delta+V_\omega\}\) in \(L^2(\mathbb{R}^d)\), \(d\geq 3\). The \(V_\omega\) are bounded random sparse potentials, not necessarily decaying. The proof is based on a criterion given by Hörmander. For deterministic potentials, this criterion was already used to prove the wave operator existence for potentials which are not decaying in some directions.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 81Q10
zbMATH DE Number: 2091494
zbMATH Keywords: absolutely continuous spectrum
zbMATH Keywords: random sparse potentials
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: wave operators
reviewed by: Michael Demuth
MaRDI profile type: Publication
full work available at URL: b:math.0000032704.88514.9c
OpenAlex ID: W2052742979
DOI: 10.1023/B:MATH.0000032704.88514.9C
description: scientific article; zbMATH DE number 2091494