DYNAMICAL SYSTEMS

AND IRREVERSIBILITY

A SPECIAL VOLUME OF ADVANCES IN CHEMICAL PHYSICS

VOLUME 122

EDITORIAL BOARD

BRUCE J. BERNE, Department of Chemistry, Columbia University, New York, New York, U.S.A.

KURT BINDER, Institut fu¨r Physik, Johannes Gutenberg-Universita¨t Mainz, Mainz, Germany

A. WELFORD CASTLEMAN, JR., Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, U.S.A.

DAVID CHANDLER, Department of Chemistry, University of California, Berkeley, California, U.S.A.

M.S. CHILD, Department of Theoretical Chemistry, University of Oxford, Oxford, U.K.

WILLIAM T. COFFEY, Department of Microelectronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland

F. FLEMING CRIM, Department of Chemistry, University of Wisconsin, Madison, Wisconsin, U.S.A.

ERNEST R. DAVIDSON, Department of Chemistry, Indiana University, Bloomington, Indiana, U.S.A.

GRAHAM R. FLEMING, Department of Chemistry, The University of California, Berkeley, California, U.S.A.

KARL F. FREED, The James Franck Institute, The University of Chicago, Chicago, Illinois, U.S.A.

PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems, Universite´ Libre de Bruxelles, Brussels, Belgium

ERIC J. HELLER, Department of Chemistry, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A.

ROBIN M. HOCHSTRASSER, Department of Chemistry, The University of Pennsylvania, Philadelphia, Pennsylvania, U.S.A.

R.KOSLOFF, The Fritz Haber Research Center for Molecular Dynamics and Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem,

Israel

RUDOLPH A. MARCUS, Department of Chemistry, California Institute of Technology,

Pasadena, California, U.S.A.

G.NICOLIS, Center for Nonlinear Phenomena and Complex Systems, Universite´ Libre de Bruxelles, Brussels, Belgium

THOMAS P. RUSSELL, Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts

DONALD G. TRUHLAR , Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A.

JOHN D. WEEKS , Institute for Physical Science and Technology and Department of Chemistry, University of Maryland, College Park, Maryland, U.S.A.

PETER G. WOLYNES , Department of Chemistry, University of California, San Diego, California, U.S.A.

DYNAMICAL SYSTEMS AND IRREVERSIBILITY: PROCEEDINGS OF THE XXI SOLVAY CONFERENCE ON PHYSICS

ADVANCES IN CHEMICAL PHYSICS

VOLUME 122

Edited by

IOANNIS ANTONIOU

International Solvay Institutes for Physics and Chemistry, Brussels, Belgium

Series Editors
I. PRIGOGINE	STUART A. RICE
Center for Studies in Statistical Mechanics	Department of Chemistry
and Complex Systems	and
The University of Texas	The James Franck Institute
Austin, Texas	The University of Chicago
and	Chicago, Illinois
International Solvay Institutes
Universite´ Libre de Bruxelles
Brussels, Belgium

AN INTERSCIENCE PUBLICATION

JOHN WILEY & SONS, INC.

This book is printed on acid-free paper.

Copyright # 2002 by John Wiley & Sons, Inc., New York. All rights reserved.

Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, [phone], fax [phone]. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, [phone], fax [phone], E-Mail: [e-mail].

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10 9 8 7 6 5 4 3 2 1

CONTRIBUTORS TO VOLUME 122

L. ACCARDI, Centro Vito Volterra, Polymathematics, Facolta di Economia, Universita degli Studi di Roma Tor Vergata, Rome, Italy

Y.AIZAWA, Department of Applied Physics, Faculty of Science and Engineering, Waseda University, Tokyo, Japan

I. ANTONIOU, International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium; and Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium

F. T. ARECCHI, Department of Physics, University of Florence, Florence, Italy; and National Institute of Applied Optics (INOA), Florence, Italy

R.BALESCU, Department of Physical Statistics–Plasma, Free University of Brussels, Brussels, Belgium

A. BOHM, Department of Physics, University of Texas, Austin, Texas, U.S.A.

LUIS J. BOYA, Center for Particle Physics, Department of Physics, The University of Texas, Austin, Texas, U.S.A. Permanent address: Department of Theoretical Physics, Faculty of Science, University of Zaragoza, Zaragoza, Spain

PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems, Free University of Brussels, Brussels, Belgium

KARL GUSTAFSON, Department of Mathematics, University of Colorado, Boulder, Colorado, U.S.A.; and International Solvay Institutes for Physics and Chemistry, University of Brussels, Brussels, Belgium

HIROSHI H. HASEGAWA, Department of Mathematical Sciences, Ibaraki University, Mito, Japan; and Center for Statistical Mechanics, University of Texas, Austin, Texas, U.S.A.

KUNIHIKO KANEKO, Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, Tokyo, Japan

E.KARPOV, Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin, Texas, U.S.A.; and International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium

S. V. KOZYREV, Centro Vito Volterra, Polymathematics, Facolta di Economia, Universita degli Studi di Roma Tor Vergata, Rome, Italy

v

vi	contributors to volume 122

MIKIO NAMIKI, Department of Physics, Waseda University, Tokyo, Japan

G.ORDONEZ, Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin, Texas, U.S.A.; and International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium

T. PETROSKY, Center for Studies in Statistical Mechanics and Complex Systems, University of Texas, Austin, Texas, U.S.A.; International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium; and Theoretical Physics Department, University of Vrije, Brussels, Belgium

I. PRIGOGINE, Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas, Austin, Texas, U.S.A.; and International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium

Z. SUCHANECKI, International Solvay Institutes for Physics and Chemistry, Free University of Brussels, Brussels, Belgium; Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium; and Institute of Mathematics, University of Opole, Opole, Poland

E. C. G. SUDARSHAN, Center for Particle Physics, Department of Physics, The University of Texas, Austin, Texas, U.S.A.

P. S ´ , Department of Physics of Complex Systems, Eo¨tvo¨s University,

ZEPFALUSY

Budapest, Hungary; and Research Institute for Solid State Physics and Optics, Budapest, Hungary

S. TASAKI, Department of Physics, Nara Women’s University, Nara, Japan; and Institute for Fundamental Chemistry, Kyoto, Japan. Present address: Department of Applied Physics and Advanced Institute for Complex Systems, Waseda University, Tokyo, Japan

H. WALTHER, Sektion Physik der Universita¨t Mu¨nchen and Max Planck Institut fu¨r Quantenoptik, Garching, Federal Republic of Germany

ADMINISTRATIVE BOARD OF THE INTERNATIONAL SOLVAY INSTITUTES FOR PHYSICS AND CHEMISTRY

J. SOLVAY President of the Administrative Board

F. BINGEN Vice-President of the Administrative Board I. PRIGOGINE Director of the Solvay Institutes

I. ANTONIOU Deputy Director of the Solvay Institutes F. LAMBERT Secretary of the Administrative Board

A.BELLEMANS Secretary of the Scientific Committee of Chemistry

M.HENNEAUX Secretary of the Scientific Committee of Physics

D.JANSSEN

A.JAUMOTTE

G. NICOLIS

J. M. PIRET

J. REISSE

R. LEFEVER

vii

SCIENTIFIC COMMITTEE FOR PHYSICS OF THE INTERNATIONAL SOLVAY INSTITUTES FOR PHYSICS AND CHEMISTRY

A. ABRAGAM	Professeur Honoraire au Colle`ge de France, Paris,
	France
P. W. ANDERSON	Department of Physics, Princeton University,
	Princeton, NJ, U.S.A.
F. T. ARECCHI	Directeur, Istituto Nazionale de Ottica Applicata,
	Florence, Italy
M. HENNEAUX	De´partement de Physique, Universite´ Libre de
	Bruxelles, Bruxelles, Belgium
I. M. KHALATNIKOFF	Russian Academy of Sciences, Landau Institute of
	Theoretical Physics, Moscow, Russia
Y. NE’EMAN	Sackler Institute for Advanced Study, Tel-Aviv
	University, Tel Aviv, Israel
D. PHILLIPS	35, Addisland Court, Holland Villas Road, London,
	England
R. Z. SAGDEEV	East West Place Science Center, University of
	Maryland, College Park, MD, U.S.A.
G. SETTI	European Southern Laboratory, Munich,
	Germany
G. t’HOOFT	Institute for Theoretical Physics, Utrecht University,
	Utrecht, Netherlands
S. C. TONWAR	Tata Institute for Fundamental Research, Bombay,
	India
H. WALTHER	Max-Planck-Institute fu¨r Quantenoptik, Mu¨nich,
	Germany
V. F. WEISSKOPF	Department of Physics, Massachusetts Institute of
	Technology, Cambridge, MA, U.S.A.

ix

THE SOLVAY CONFERENCES ON PHYSICS

The Solvay conferences started in 1911. The first conference on radiation theory and the quanta was held in Brussels. This was a new type of conference and it became the tradition of the Solvay conference; the participants are informed experts in a given field and meet to discuss one or a few mutually related problems of fundamental importance and seek to define the steps for the solution.

The Solvay conferences in physics have made substantial contributions to the development of modern physics in the twentieth century.

1.(1911) ‘‘Radiation theory and the quanta’’

2.(1913) ‘‘The structure of matter’’

3.(1921) ‘‘Atoms and electrons’’

4.(1924) ‘‘Electric conductivity of metals’’

5.(1927) ‘‘Electrons and photons’’

6.(1930) ‘‘Magnetism’’

7.(1933) ‘‘Structure and properties of the atomic nuclei’’

8.(1948) ‘‘Elementary particles’’

9.(1951) ‘‘Solid state’’

10.(1954) ‘‘Electrons in metals’’

11.(1958) ‘‘The structure and evolution of the universe’’

12.(1961) ‘‘The quantum theory of fields’’

13.(1964) ‘‘The structure and evolution of galaxies’’

14.(1967) ‘‘Fundamental problems in elementary particle physics’’

15.(1970) ‘‘Symmetry properties of nuclei’’

16.(1973) ‘‘Astrophysics and gravitation’’

17.(1978) ‘‘Order and fluctuations in equilibrium and nonequilibrium statistical mechanics’’

18.(1982) ‘‘High-energy physics. What are the possibilities for extending our understanding of elementary particles and their interactions to much greater energies?’’

19.(1987) ‘‘Surface science’’

20.(1991) ‘‘Quantum optics’’

21.(1998) ‘‘Dynamical systems and irreversibility’’

For more information, visit the website of the Solvay Institutes http://solvayins.ulb.ac.be

xi

XXIst INTERNATIONAL SOLVAY CONFERENCE IN PHYSICS, KEIHANNA PLAZA, NOVEMBER 1–5, 1998 DYNAMICAL SYSTEMS AND IRREVERSIBILITY

(Top row) M. Miyamoto, H. Takahashi, H. Nakazato, G. Ordonez, H. Fujisaka, S. Sasa, H. Hasegawa, Y. Ootaki, A. Oono (Fourth row from bottom) M. Gadella, A. Bohm, R. Willox, K. Sekimoto, T. Arimitsu, K. Kaneko, D. Driebe, S. Tasaki, Y. Ichikawa (Third row from bottom) F. Lambert, K. Gustafson, J. R. Dorfman, M.Ernst, S. Pascazio, T. Hida, B. Pavlov, Y. Aizawa, Yu. Melnikov, T. Petrosky, A. Awazu (Second row from bottom) K. Kitahara, Ya. Sinai, I. Antoniou, L. Accardi, H. Hegerfeldt, O’Dae Kwon, P. Szepfalusy, M. Namiki, L. Boya, K. Kawasaki, H. Posch, P. Gaspa (Bottom row) R. Balescu, Hao Bai-lin, H. Mori, H. Walther, J. Kondo, I. Prigogine, J. Solvay, L. Reichl, N. G. van Kampen, T. Arecchi, S. C. Tonwar

CONTENTS

Administrative Board of the International Solvay
Institutes for Physics and Chemistry	vii
Scientific Committee for Physics of the International
Solvay Institutes for Physics and Chemistry	ix
The Solvay Conferences on Physics	xi
Preface	xv
Opening Speech by J. Solvay	xvii
Introductory Remarks by Ilya Prigogine	xxi
PART ONE
DISCRETE MAPS
Non-Markovian Effects in the Standard Map	3
By R. Balescu
Thermodynamics of a Simple Hamiltonian Chaotic System	21
By Hiroshi H. Hasegawa
Harmonic Analysis of Unstable Systems	33
By I. Antoniou and Z. Suchanecki
Properties of Permanent and Transient Chaos in Critical States	49
By P. Sze´pfalusy
From Coupled Dynamical Systems to Biological Irreversibility	53
By Kunihiko Kaneko
PART TWO
TRANSPORT AND DIFFUSION
Irreversibility in Reversible Multibaker Maps —Transport
and Fractal Distributions	77
By S. Tasaki
Diffusion and the Poincare´–Birkhoff Mapping
of Chaotic Systems	109
By Pierre Gaspard
	xiii

xiv	contents
Transport Theory for Collective Modes and Green–Kubo
Formalism for Moderately Dense Gases		129
By T. Petrosky
New Kinetic Laws of Cluster Formation in N-Body
Hamiltonian Systems		161
By Y. Aizawa
PART THREE
QUANTUM THEORY, MEASUREMENT, AND DECOHERENCE
Quantum Phenomena of Single Atoms		167
By H. Walther
Quantum Superpositions and Decoherence: How to Detect
Interference of Macroscopically Distinct Optical States		199
By F. T. Arecchi and A. Montina
Quantum Decoherence and the Glauber Dynamics from the
Stochastic Limit		215
By L. Accardi and S. V. Kozyrev
CP Violation as Antieigenvector-Breaking		239
By K. Gustafson
PART FOUR
EXTENSION OF QUANTUM THEORY AND FIELD THEORY
Dynamics of Correlations. A Formalism for Both Integrable
and Nonintegrable Dynamical Systems		261
By I. Prigogine
Generalized Quantum Field Theory		277
By E. C. G. Sudarshan and Luis J. Boya
Age and Age Fluctuations in an Unstable Quantum System		287
By G. Ordonez, T. Petrosky, and E. Karpov
Microphysical Irreversibility and Time Asymmetric Quantum
Mechanics		301
By A. Bohm
Possible Origins of Quantum Fluctuation Given by
Alternative Quantization Rules		321
By Mikio Namiki
Author Index		331
Subject Index		339

PREFACE

This volume contains the contributions to the XXIst Solvay Conference on Physics, which took place at the Keihanna Interaction Plaza in the Kansaı¨ Science City. The topic was Dynamical Systems and Irreversibility.

The conference has been made possible thanks to the support of the Keihanna Foundation, the Honda Foundation, and the International Solvay Institutes for Physics and Chemistry, founded by E. Solvay.

Ioannis Antoniou

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