Open Quantum Systems I The Hamiltonian Approach
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge.
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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
1880
S. Attal · A. Joye · C.-A. Pillet (Eds.)
Open Quantum Systems I The Hamiltonian Approach
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Editors Stéphane Attal Institut Camille Jordan Universit é Claude Bernard Lyon 1 21 av. Claude Bernard 69622 Villeurbanne Cedex France e-mail: [email protected]
Alain Joye Institut Fourier Universit é de Grenoble 1 BP 74 38402 Saint-Martin d'Hères Cedex France e-mail: [email protected]
Claude-Alain Pillet CPT-CNRS, UMR 6207 Université du Sud Toulon-Var BP 20132 83957 La Garde Cedex France e-mail: [email protected] Library of Congress Control Number: 2006923432 Mathematics Subject Classification (2000): 37A60, 37A30, 47A05, 47D06, 47L30, 47L90, 60H10, 60J25, 81Q10, 81S25, 82C10, 82C70 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISBN-10 3-540-30991-8 Springer Berlin Heidelberg New York ISBN-13 978-3-540-30991-8 Springer Berlin Heidelberg New York DOI 10.1007/b128449 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, 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. A EX package Typesetting: by the authors and SPI Publisher Services using a Springer LT Cover design: design & production GmbH, Heidelberg
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543210
Preface
This is the first in a series of three volumes dedicated to the lecture notes of the Summer School ”Open Quantum Systems” which took place at the Institut Fourier in Grenoble from June 16th to July 4th 2003. The contributions presented in these volumes are revised and expanded versions of the notes provided to the students during the School. Closed vs. Open Systems By definition, the time evolution of a closed physical system S is deterministic. It is usually described by a differential equation x˙ t = X(xt ) on the manifold M of possible configurations of the system. If the initial configuration x0 ∈ M is known then the solution of the corresponding initial value problem yields the configuration xt at any future time t. T
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