Result: Characterization of the Anderson Metal―Insulator Transition for Non Ergodic Operators and Application

Title:
Characterization of the Anderson Metal―Insulator Transition for Non Ergodic Operators and Application
Authors:
ROJAS-MOLINA, Constanza
Source:
Annales Henri Poincaré. 13(7):1575-1611
Publisher Information:
Heidelberg: Springer, 2012.
Publication Year:
2012
Physical Description:
print, 33 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Physics, Physique, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Théorie des opérateurs, Operator theory, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Analyse stochastique, Stochastic analysis, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Bootstrap, Ergodicité, Ergodicity, Ergodicidad, Impureté, Impurities, Localisation, Localization, Localización, Modélisation, Modelling, Métal, Metals, Opérateur Schrödinger, Schrödinger operator, Operador Schrodinger, Physique mathématique, Mathematical physics, Potentiel, Potentials, Solide, Solids, Treillis, Lattice, Enrejado, 06Bxx, 35J10, 37A25, 47B80, 60Fxx, 60H25, 62F40, Analyse multiéchelle, Opérateur aléatoire
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Université de Cergy-Pontoise UMR CNRS 8088, 95000 Cergy-Pontoise, France
ISSN:
1424-0637
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=26385819
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics

Theoretical physics
Accession Number:
edscal.26385819
Database:
PASCAL Archive

Further Information

We study the Anderson metal-insulator transition for non ergodic random Schrödinger operators in both annealed and quenched regimes, based on a dynamical approach of localization, improving known results for ergodic operators into this more general setting. In the procedure, we reformulate the Bootstrap Multiscale Analysis of Germinet and Klein to fit the non ergodic setting. We obtain uniform Wegner Estimates needed to perform this adapted Multiscale Analysis in the case of Delone-Anderson type potentials, that is, Anderson potentials modeling aperiodic solids, where the impurities lie on a Delone set rather than a lattice, yielding a break of ergodicity. As an application we study the Landau operator with a Delone-Anderson potential and show the existence of a mobility edge between regions of dynamical localization and dynamical delocalization.