Localization for random Schrödinger operators on \(L^ 2 (\mathbb{R}^ d)\): a semiclassical model
type: Item
instance of: scholarly article
title: Localization for random Schrödinger operators on \(L^ 2 (\mathbb{R}^ d)\): a semiclassical model
zbMATH Open document ID: 0817.35088
author: Frédéric Klopp
publication date: 1995-04-18T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75117
review text: In \(L^ 2 ({\mathbb{R}}^ d)\), we prove exponential localization for a semi- classical periodic Schrödinger operator perturbated by small independent identically distributed random perturbations put in each well of the periodic potential. To do this, we first show that our operator, restricted to some suitably chosen energy interval, is unitarily equivalent to an infinite random matrix with coefficients we can control. Then, for this type of random matrices, we prove an Anderson localization theorem. We also apply this result to prove localization at large energy or large disorder, for long range discrete Anderson models.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 81Q20
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 47B80
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 15B52
Mathematics Subject Classification ID: 35R60
zbMATH DE Number: 745228
zbMATH Keywords: random perturbations
zbMATH Keywords: infinite random matrix
zbMATH Keywords: Anderson localization theorem
zbMATH Keywords: discrete Anderson models
MaRDI profile type: Publication
OpenAlex ID: W2070078559
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DOI: 10.5802/AIF.1456
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 745228