On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials
type: Item
instance of: scholarly article
title: On the integrated density of states for the Schrödinger operators with certain random electromagnetic potentials
zbMATH Open document ID: 0820.35152
author: Hiroyuki Matsumoto
published in: Journal of the Mathematical Society of Japan
publication date: 1995-09-21T00:00:00Z
review text: The author considers a family of random Schrödinger operators with magnetic fields. Such operators arise in quantum models of disordered systems. Spectral properties of such operators and the so-called integrated density of states (IDS) are investigated. The main purpose of this paper is to study the asymptotic behaviour of the IDS (Lifshitz type asymptotics) for two types of the random Schrödinger operators. The author uses the functional analytic methods. He uses the Cwikel-Lieb- Rosenbljum and Lieb-Thirring bounds for the number of negative eigenvalues of Schrödinger operators to prove the upper estimates for the IDS. Recently Ueki (preprint) following the path integral approach has studied a similar problem and obtained similar results.
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 35P15
zbMATH DE Number: 469058
zbMATH Keywords: integrated density
zbMATH Keywords: random Schrödinger operators
zbMATH Keywords: quantum models of disordered systems
reviewed by: Wiesław Kotarski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04520197
OpenAlex ID: W1992601397
DOI: 10.2969/JMSJ/04520197
description: scientific article; zbMATH DE number 469058