Mathematical Results In Quantum Physics: Proceedings of the QMath11 Conference PDF
Preview Mathematical Results In Quantum Physics: Proceedings of the QMath11 Conference
Mathematical Results in QUANTUM PHYSICS edited by Pavel Exner World Scientific Proceedings of the QMath11 Conference Mathematical Results in QUANTUM PHYSICS Hradec Králové, Czech Republic 6 – 10 September 2010 edited by Pavel Exner Doppler Institute, Prague, Czech Republic World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8147.9789814350358-tp.indd 1 4/20/11 5:31 PM Mathematical Results in QUANTUM PHYSICS edited by Pavel Exner 8147.9789814350358-tp.indd 2 4/20/11 5:31 PM This page is intentionally left blank Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. MATHEMATICAL RESULTS IN QUANTUM PHYSICS (With DVD-ROM) Proceedings of the QMath11 Conference Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4350-35-8 ISBN-10 981-4350-35-4 Printed in Singapore. LaiFun - Mathematical Results in Qaun Phys.pm1d 4/11/2011, 2:51 PM April1,2011 17:10 WSPC-ProceedingsTrimSize:9.75inx6.5in QMath11proc v PREFACE Conference series are more than just collections of scientific meetings; they make it possible to follow the life of a community of people with shared interest over a certainperiodof time. True,very few series reachthe state ofeffective immortality spanning several generations; most of them die at a young age due to the lack of peoplewillingtotaketheburdenoforganizingsuchameeting,ataskwhichusually distracts you from your normal activity for months if not more. The QMath series has managed to pass its teens and enter the third decade of its existence. It was begotten in 1987 in Dubna as an attempt to foster fruitful collaboration between mathematical physicists from different parts of the world; its midwives did not suspect at the beginning that within just a couple of years their working conditions will change beyond any expectation. The series proved to have a strong enough motivation, however, to survive in the new conditions, with the periodicity which stabilized after some time to three years, and its meetings convened at different places, mostly in Europe but also once in Mexico. The eleventh issue returned to the Czech Republic where the meeting was held twice before. This time the town of Hradec Kr´alov´e was chosen as its site which gavethe participants the opportunity to enjoy its historicalcenter, a shortwalking distance from the new university building where the conference took place. The main sponsor of the meeting was Doppler Institute for Mathematical Physics and Applied Mathematics,acenterofbasicresearchsupportedbytheCzechgovernment and we also enjoyed support from the European project CZ.1.07/2.3.00/09.0044; we appreciate the financial help which made it possible to keep the registrationfee at a reasonable level. We are also grateful to the Doppler Institute institutional constituents, Czech Technical University, Nuclear Physics Institute of the Czech AcademyofSciences,andinthe firstplace,toUniversityofHradecKr´alov´efor the organizationalsupport they provided. Theplenarylecturesweredevotedtothepropertiesofquantumsystems,bothin the one-body and many-body situations, quantum information, and related math- ematicalproblems. With three exceptions their contents are reflected in the papers collectedin the firstpartofthis book.The secondpartsummarizes the topicalses- sions contents, featuring most of the invited talks. These six sessions were devoted tothespectraltheory,many-bodyquantumsystems,quantumchaos,quantumfield theory,quantuminformationand,motivatedbysomerecentintriguingobservations, we have also included a session on the physics of social systems. The talks not in- cluded,both invitedandcontributedones,arepresentthroughtheir abstracts,and April1,2011 17:10 WSPC-ProceedingsTrimSize:9.75inx6.5in QMath11proc vi moreover, the volume is accompanied with a dvd containing most of the presenta- tions as they appeared on the screen during the talks. The seventh session was special, being devoted to the important jubilee of Ari Laptev in appreciation of his work for the mathematical physics community, both through his mathematicalpapers and by organizingnumerous scientific events. We wished him good health, happiness, and many new interesting results. IhopethereaderofthisvolumewillhavenodoubtthattheQMath11 conference offered a rich and interesting programme which its participants enjoyed. I want to thankheretothosewhomadethispossible:tothe(other)membersofthescientific and local organizing committees, to the topical session organizers, to the student volunteers and all the others who helped. With the eleventh issue of the series behind us, we firmly hope it will not be the last one. Prague, January 2011 Pavel Exner April1,2011 17:10 WSPC-ProceedingsTrimSize:9.75inx6.5in QMath11proc vii CONFERENCE COMMITTEES SCIENTIFIC COMMITTEE Maria Jesus Esteban Ari Laptev Jakob Yngvason Pavel Exner Petr Sˇeba LOCAL ORGANIZING COMMITTEE Petr Sˇeba, chair Pavel Exner Ivo Volf Jaroslav Dittrich Jan Kˇr´ıˇz,secretary This page is intentionally left blank April1,2011 17:10 WSPC-ProceedingsTrimSize:9.75inx6.5in QMath11proc ix CONTENTS Preface v Conference Committees vii Part A Plenary Talks 1 Relative entropies and entanglement monotones 3 Nilanjana Datta Binding, stability, and non-binding of multi-polaron systems 21 Rupert L. Frank, Elliott H. Lieb, Robert Seiringer, Lawrence E. Thomas Interacting electrons on the honeycomb lattice 33 Alessandro Giuliani Renormalization of Dirac’s polarized vacuum 45 Mathieu Lewin Convergence results for thick graphs 60 Olaf Post Spectral Properties of Wigner Matrices 79 Benjamin Schlein Lieb-Robinson bounds and quasi-locality for the dynamics of many-body quantum systems 95 Robert Sims Disorder-induced delocalization on tree graphs 107 Michael Aizenman, Simone Warzel Semiclassical spectral bounds and beyond 110 Timo Weidl
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