Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
type: Item
instance of: scholarly article
title: Existence of the density of states for multi-dimensional continuum Schrödinger operators with Gaussian random potentials
zbMATH Open document ID: 0898.47029
author: Werner Fischer
author: Thomas Hupfer
author: Hajo Leschke
author: Peter Müller
published in: Communications in Mathematical Physics
publication date: 1998-02-25T00:00:00Z
review text: The spectral-averaging technique is used to prove the absolute continuity of the integrated density of states for a Schrödinger operator with a rather general Gaussian random potential in multidimensional Euclidean space. As a consequence, an explicit upper bound for the density of states is derived. The result is based on the Wegner estimate [\textit{F. Wegner}, Z. Phys. B 44, 9-15 (1981)] which is proved to hold for all continuum Schrödinger operators whose random potential admits a certain one-parameter decomposition. The present paper accomplishes partly the localization proofs announced by the authors in \textit{W. Fischer}, \textit{H. Leschke} and \textit{P. Müller} [Lett. Math. Phys. 38, No. 4, 343-348 (1996; Zbl 0862.60047)]. The authors remark their results can be extended to random Schrödinger operators with rather general magnetic fields.
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 1121344
zbMATH Keywords: continuum Schrödinger operators
zbMATH Keywords: random potentials
zbMATH Keywords: Wegner estimate
zbMATH Keywords: density of states
zbMATH Keywords: Gaussian random potentials
reviewed by: Pavel Dyshlovenko
MaRDI profile type: Publication
full work available at URL: s002200050236
OpenAlex ID: W2005752837
DOI: 10.1007/S002200050236
description: scientific article; zbMATH DE number 1121344