Effective Evolution Equations from Quantum Dynamics
These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the deriv
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Niels Benedikter Marcello Porta Benjamin Schlein
Effective Evolution Equations from Quantum Dynamics 123
SpringerBriefs in Mathematical Physics Volume 7
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Niels Benedikter Marcello Porta Benjamin Schlein •
Effective Evolution Equations from Quantum Dynamics
123
Niels Benedikter Department of Mathematical Sciences University of Copenhagen Copenhagen Denmark
Benjamin Schlein Institute of Mathematics University of Zurich Zurich Switzerland
Marcello Porta Institute of Mathematics University of Zurich Zurich Switzerland
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-3-319-24896-7 ISBN 978-3-319-24898-1 (eBook) DOI 10.1007/978-3-319-24898-1 Library of Congress Control Number: 2015950862 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2016 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
Preface
In these notes we review the material presented at the summer school on “Mathematical Physics, Analysis and Stochastics” held at the University of Heidelberg in July 2014. We consider the time evolution of quantum systems and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. We would like to thank Manfred Salmhofer and Christoph Kopper for organizing the summer school “Mathematical Physics, Analysis and Stochastics” and for encouraging us to write up these notes. The work of Marcello Porta and of Benjamin Schlein has been supported by the ERC grant MAQD-240518. Niels Benedikter has been partially supported by t
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