Quantum Probability and Infinite Dimensional Analysis

314 Pages·2010·2.133 MB·English

by  Ouerdiane H., Barhoumi A. (eds.)

QQ uantum
PProbability

and Infinite Dimensional Analysis
Proceedings of the 29th Conference
QP–PQ: Quantum Probability and White Noise Analysis*
Managing Editor: W. Freudenberg
Advisory Board Members: L. Accardi, T. Hida, R. Hudson and
K. R. Parthasarathy
QP–PQ: Quantum Probability and White Noise Analysis
Vol. 26: Quantum Bio-Informatics III
From Quantum Information to Bio-Informatics
eds. L. Accardi, W. Freudenberg and M. Ohya
Vol. 25: Quantum Probability and Infinite Dimensional Analysis
Proceedings of the 29th Conference
eds. H. Ouerdiane and A. Barhoumi
Vol. 24: Quantum Bio-Informatics II
From Quantum Information to Bio-informatics
eds. L. Accardi, W. Freudenberg and M. Ohya
Vol. 23: Quantum Probability and Related Topics
eds. J. C. García, R. Quezada and S. B. Sontz
Vol. 22: Infinite Dimensional Stochastic Analysis
eds. A. N. Sengupta and P. Sundar
Vol. 21: Quantum Bio-Informatics
From Quantum Information to Bio-Informatics
eds. L. Accardi, W. Freudenberg and M. Ohya
Vol. 20: Quantum Probability and Infinite Dimensional Analysis
eds. L. Accardi, W. Freudenberg and M. Schürmann
Vol. 19: Quantum Information and Computing
eds. L. Accardi, M. Ohya and N. Watanabe
Vol. 18: Quantum Probability and Infinite-Dimensional Analysis
From Foundations to Applications
eds. M. Schürmann and U. Franz
Vol. 17: Fundamental Aspects of Quantum Physics
eds. L. Accardi and S. Tasaki
Vol. 16: Non-Commutativity, Infinite-Dimensionality, and Probability
at the Crossroads
eds. N. Obata, T. Matsui and A. Hora
Vol. 15: Quantum Probability and Infinite-Dimensional Analysis
ed. W. Freudenberg
Vol. 14: Quantum Interacting Particle Systems
eds. L. Accardi and F. Fagnola
Vol. 13: Foundations of Probability and Physics
ed. A. Khrennikov
*For the complete list of the published titles in this series, please visit:
www.worldscibooks.com/series/qqpwna_series.shtml
QP–PQ
Quantum Probability and White Noise Analysis
Volume XXV
QQ
uantum
PP
robability

and Infinite Dimensional Analysis
Proceedings of the 29th Conference
Hammamet, Tunisia 13 – 18 October 2008
Editors
H Ouerdiane

University of Tunis El Manar, Tunisia
A Barhoumi

University of Sousse, Tunisia
World Scientific
NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI
• • • • • • •
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Conference on Quantum Probability and Infinite Dimensional Analysis (29th : 2008 : Hammamet,
Tunisia)
Quantum probability and infinite dimensional analysis : proceedings of the 29th conference,
Hammamet, Tunisia 13-18 October 2008 / edited by H. Ouerdiane & A. Barhoumi.
p. cm. -- (QP-PQ, quantum probability and white noise analysis ; v. 25)
Includes bibliographical references and index.
ISBN-13: 978-981-4295-42-0 (hardcover : alk. paper)
ISBN-10: 981-4295-42-6 (hardcover : alk. paper)
1. Stochastic analysis--Congresses. 2. Probabilities--Congresses. 3. Mathematical physics--
Congresses. I. Ouerdiane, Habib. II. Barhoumi, A. (Abdessatar) III. Title.
QA274.2.C66 2008
519.2'2--dc22
2009048003
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2010 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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Printed in Singapore.
v
PREFACE
This volume constitutes the proceedings of the 29th Conference on
QuantumProbabilityandRelatedTopicsheldinHammamet,Tunisia,Oc-
tober13-18,2008.Thiswasthefirsttimethisimportantinternationalevent
tookplaceintheAfrica.ThisProceedingsvolumecontainstwentyrefereed
researcharticles.Almost120mathematiciansandphysicalmathematicians
participated in this conference from all over the world. This volume will be
of interest to professional researchers and graduate students who will gain
a perspective on current activity and background in the topics covered.
Thegoaloftheconferencewastocommunicatenewresultsinthefields
of quantum probability and infinite dimensional analysis, to bring together
scientistswithdifferentbackgroundswhoworkinrelatedfields,andtostim-
ulate new collaborations. The fact that contributions to this volume range
from quantum probability, white noise and stochastic analysis, orthogo-
nal polynomials and interacting Fock spaces, free probability and random
matrices, quantum information, quantum statistics, control and filtering,
L´evy processes, mathematical models in biology and foundation of quan-
tum mechanics shows that research in quantum probability is very active
and strongly involved in modern mathematical developments and applica-
tions.
The organizers of the conference were extremely happy to see many
eminentmathematicianshavingcontributedtothesuccessoftheconference
and cultivated new ideas. We would like to thank all participants for their
hard work and for helping to create a very stimulating atmosphere. To our
great pleasure, important papers presented at the conference are published
in this volume. As such, we are grateful to the respective authors and to
the anonymous referees for their efficient help in evaluating each paper in
this collection. We also express our deep appreciation to World Scientific
Publishing, in particular to Ms E. H. Chionh as their acting representative
for a remarkably pleasant cooperation.
WeacknowledgegratefullythegeneralsupportoftheTunisianMinistry
of Higher Education Scientific Research and Technology, the Association
ofInfiniteDimensionalAnalysisandQuantumProbability(AQPIDA),the
vi Preface
TunisianMathematicalSociety,theUniversityofTunisElManarandother
Tunisian Research Institutes.
Finallywehopethatthisconferencehascontributednotonlytopromote
scientific activities but also to mutual international understanding.
The editors:
Abdessatar Barhoumi Hammamet, Tunisia
(Sousse University, Tunisia) November 2009
Habib Ouerdiane
(Tunis El-Manar University, Tunisia)
vii
CONTENTS
Preface v
On the Central Extensions of the Heisenberg Algebra 1
L. Accardi & A. Boukas
Representations of the L´evy-Meixner Oscillator Algebra
and the Overcompleteness of the Associated Sequences of
Coherent States 13
A. Barhoumi, H. Ouerdiane & A. Riahi
Some Systems of Dualities in White Noise Analysis 32
T. Hida
Quantum White Noise Derivatives and Associated
Differential Equations for White Noise Operators 42
U.C. Ji & N. Obata
The Gibbs Conditioning Principle for White Noise Distribu-
tions: Interacting and Non-Interacting Cases 55
F. Cipriano, S. Gheryani & H. Ouerdiane
Markov Triplets on CAR Algebras 71
J. Pitrik
Quantum Fokker-Planck Models: Limiting Case in the
Lindblad Condition 87
F. Fagnola & L. Neumann
Generalized Euler Heat Equation 99
A. Barhoumi, H. Ouerdiane & H. Rguigui
viii Contents
On Quantum De Finetti’s Theorems 117
V. Crismale & Y.G. Lu
Kolmogorovian Model for EPR-Experiment 128
D. Avis, P. Fischer, A. Hilbert & A. Khrennikov
Free White Noise Stochastic Equation 138
L. Accardi, W. Ayed & H. Ouerdiane
L´evy Models Robustness and Sensitivity 153
F. E. Benth, G. Di Nunno & A. Khedher
Quantum Heat Equation with Quantum K-Gross Laplacian:
Solutions and Integral Representation 185
S. Horrigue & H. Ouerdiane
On Marginal Markov Processes of Quantum Quadratic
Stochastic Processes 203
F. Mukhamedov
On the Applicability of Multiplicative Renormalization
Method for Certain Power Functions 216
I. Kubo, H.-H. Kuo & S. Namli
Convolution Equation: Solution and Probabilistic Representation 230
J. L. Da Silva, M. Erraoui & H. Ouerdiane
From Classical to Quantum Entropy Production 245
F. Fagnola & R. Rebolledo
Extending the Set of Quadratic Exponential Vectors 262
L. Accardi, A. Dhahri & M. Skeide
On Operator-Parameter Transforms Based on Nuclear Alge-
bra of Entire Functions and Applications 267
A. Barhoumi, H. Ouerdiane, H. Rguigui & A. Riahi
Contents ix
Dissipative Quantum Annealing 288
D. de Falco, E. Pertoso & D. Tamascelli
Author Index 303