Anderson localization for multi-dimensional systems at large disorder or large energy
type: Item
instance of: scholarly article
title: Anderson localization for multi-dimensional systems at large disorder or large energy
zbMATH Open document ID: 0576.60053
DOI: 10.1007/BF01217724
author: François Delyon
author: Bernard Souillard
author: Y. Levy
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: The multidimensional discrete Schrödinger (self-adjoint) operator H acting on \(I^ 2(Z^ d)\) is defined by: \((H\Psi)(x)=-\sum_{| x- y| =1}\Psi (y)+V(x)\Psi (x)\) where \(\{V(x)\}_{x\in Z^ d}\) is a random potential chosen with a probability distribution P. It is proven for a large class of probability distributions that, with probability one, H has only pure point spectrum of multiplicity one and exponentially decaying eigenfunctions. This result holds all over the spectrum at large disorder (large V) or for large energy (eigenvalue) for a smaller disorder.
Mathematics Subject Classification ID: 60H25
zbMATH DE Number: 3921648
zbMATH Keywords: random Schrödinger equations
zbMATH Keywords: localization
zbMATH Keywords: random potential
zbMATH Keywords: exponentially decaying eigenfunctions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01217724
OpenAlex ID: W2035529122
description: scientific article; zbMATH DE number 3921648