Multi-scale Analysis for Random Quantum Systems with Interaction

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of severa

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Victor Chulaevsky Yuri Suhov

Multi-scale Analysis for Random Quantum Systems with Interaction

Progress in Mathematical Physics Volume 65 Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA Editorial Board C. Berenstein, University of Maryland, College Park, USA Sir M. Berry, University of Bristol, UK P. Blanchard, University of Bielefeld, Germany M. Eastwood, Uiversity of Adelaide, Australia A.S. Fokas, University of Cambridge, UK F. W. Hehl, University of Cologne, Germany and University of Missouri-Columbia, USA D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA

For further volumes: http://www.springer.com/series/4813

Victor Chulaevsky • Yuri Suhov

Multi-scale Analysis for Random Quantum Systems with Interaction

Victor Chulaevsky Département de Mathématiques Université de Reims Champagne-Ardenne Reims, France

Yuri Suhov Statistical Laboratory University of Cambridge Cambridge, UK

ISSN 1544-9998 ISSN 2197-1846 (electronic) ISBN 978-1-4614-8225-3 ISBN 978-1-4614-8226-0 (eBook) DOI 10.1007/978-1-4614-8226-0 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013950173 Mathematics Subject Classification (2010): 47B80, 47A75, 81Q10, 60H25, 35P10 © Springer Science+Business Media New York 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or