Quantum Probability and Applications to the Quantum Theory of Irreversible Processes
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Quantum Probability and Applications to the Quantum Theory of Irreversible Processes Proceedings of the International Workshop held at Villa Mondragone, Italy, September 6-11, 1982
Edited by L Accardi, A. Frigerio and V. Gorini
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Editors
Luigi Accardi Oipartimento di Matematica, Universita di Roma II La Romanina, 00173 Roma, Italy Alberto Frigerio Vittorio Gorini Oipartimento di Fisica, Sezione di Fisica Teorica, Universita di Milano via Celoria 16, 20133 Milano, Italy
AMS Subject Classifications (1980): 46L50, 46L55, 46L60, 47005, 47007,47045, 60G,60H, 60J, 81 B, 81 C20, 82A05, 82A 15 ISBN 3-540-12915-4 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-12915-4 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
I N T ROD U C T ION
The Workshop on Quantum Probability and Applications to the Quantum Theory of Irreversible Processes was held in Villa Mondragone, September 6 - 11, 1982. It was organized by the Department of Mathematics of the University of Rome II and by the Department of Physics of the University of Milan, with the financial support of the CNR National Group
of
Functional Analysis and Applications. Its goal was to present a survey of the present status of the topics mentioned in the title. We would like to thank the sponsoring institutions, the lecturers, and the participants for their contributions to the success of the conference.
Luigi Accardi Alberto Frigerio Gorini
Contents
L. Accardi - Some trends and problems in quantum probability. R. Alicki - scattering theory for quantum dynamical semigroups.
20
C. Barnett, R.F. Streater, I. F. Wilde. Quantum stochastic processes.
32
O. Bratteli - On dynamical semigroups and compact group actions.
46
G. Casati - Irreversibility and chaos in quantum systems.
62
C. Cecchini - Noncommutative integration and conditioning.
76
Ph. Combe, R. Rodriguez, M. Sirugue, M. Sirugue-Collin - Stochastic representation of thermal functionals.
86
C. D'Antoni - Statistical independence of local algebras.
93
D. de Falco - On the problem of nonconfigurational observables in stochastic mechanics. . 103 R. Dllmcke - Markovian limits of multi-time correlation functions for open quantum systems. . • . . . . . . . • • . . . . . . . . . •
• 1 13
A. Frigerio, V. Gorini - On stationary Markov dilations of quantum dynamical semigroups. . . . . . . . . . . . . • . . . . . • .
119
N. Gisin - A model of irreversible deterministic q
