Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential
type: Item
instance of: scholarly article
title: Anderson localization for Schrödinger operators on \(\mathbb{Z}^2\)with quasi-periodic potential
zbMATH Open document ID: 1022.47023
DOI: 10.1007/BF02392795
author: Michael Goldstein
author: W. Schlag
author: Jean Bourgain
published in: Acta Mathematica
publication date: 2002-10-21T00:00:00Z
review text: The present paper was written earlier than the authors' [Commun. Math. Phys. 220, 583-621 (2001; Zbl 0994.82044)] in which a stronger result on the title problem than in the present paper was obtained by a different proof method. Although the cited paper is selfconsistent, the present paper develops the situation in greater detail preparing the main result (Theorem 6.2). Several lemmata and propositions concerning partial problems are proved and nine figures help to understand it. Moreover, in the final section the concept of semialgebraic sets is introduced and three theorems, proved elsewhere, are stated.
reviewed by: K.-E. Hellwig
Mathematics Subject Classification ID: 47B39
Mathematics Subject Classification ID: 82B44
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 1786646
zbMATH Keywords: lattice Schödinger operator
zbMATH Keywords: discrete \({\mathcal Z}^2\)-model
zbMATH Keywords: Thouless formula
zbMATH Keywords: large deviation
zbMATH Keywords: large disorder
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1786646