Quantum Probability and Applications III Proceedings of a Conference
These proceedings of the first Quantum Probability meeting held in Oberwolfach is the fourth in a series begun with the 1982 meeting of Mondragone and continued in Heidelberg ('84) and in Leuven ('85). The main topics discussed were: quantum stochastic ca
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1303 L. Accardi W von Waldenfels (Eds.)
Quantum Probability and Applications III Proceedings of a Conference held in Oberwolfach, FRG, January 25-31, 1987
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo
Editors
Luigi Accardi Dipartimento di Matematica, Universita di Roma II Via Orazio Raimondo, 00173, Roma, Italy Wilhelm von Waldenfels Institut fur Angewandte Mathematik, Universitat Heidelberg 1m Neuenheimer Feld 294, 6900 Heidelberg, Federal Republic of Germany
Mathematics Subject Classification (1980): 43A35, 46LXX, 46M20, 47DXX, 60FXX, 60GXX, 60HXX, 60JXX, 80A05, 81 C20, 81 K05, 81 L05, 81 M05, 82A 15, 83C40, 83C75
ISBN 3·540·18919-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18919-X Springer-Verlag New York Berlin Heidelberg 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyriob! I ...
© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Introduction This volume contains the proceedings of the first Quantum Probability meeting held in Oberwolfach which is the fourth of a series begun with the 1982 meeting of Mondragone and continued in Heidelberg ('84) and in Leuven ('85). The main topics discussed during the meeting were: quantum stochastic calculus, mathematical models of quantum noise and their applications to quantum optics, the quantum Feynman-Kac formula, quantum probability and models of quantum statistical mechanics, the notion of conditioning in quantum probability and related problems (dilations, quantum Markov processes), quantum central limit theorems. We are grateful to the Mathematisches Forschungsinstitut Oberwolfach and to its director Prof. M. Barner for giving us the unique opportunity of scientific collaboration and mutual exchange. We would like to thank also the speakers and all the participants for their contributions to the vivid and sometimes heated discussions.
L. Accardi W. v. Waldenfels
CONTENTS
L. Accardi, A Note on Meyer's Note
1
L. Accardi and F. Fagnola, Stochastic Integration...............
6
D. Applebaum, Quantum Stochastic Parallel Transport on Non-Commutative Vector Bundles
20
A. Barchielli, Input and Output Channels in Quantum Systems and Quantum Stochastic Differential Equations
37
C. Cecchini, Some Noncommutative Radon-Nikodym Theorems on von Neumann Algebras
52
M. Evans and R.L. Hudson, Multidimensional Quantum Diffusions ...
69
M. Fannes, An Application of de Finetti's Theorem
89
G.W. Ford, The Quantum Langevin Equation from the Indepen
