Table Of ContentMathematical 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
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Mathematical Results in
QUANTUM PHYSICS
edited by Pavel Exner
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Published by
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USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
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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,
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the publisher.
ISBN-13 978-981-4350-35-8
ISBN-10 981-4350-35-4
Printed in Singapore.
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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
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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
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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
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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
