Deterministic Chaos in Infinite Quantum Systems

2012-12-06

The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov ...

Author: Fabio Benatti

Publisher: Springer Science & Business Media

ISBN: 9783642849992

Category: Science

Page: 225

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The purpose of this volume is to give a detailed account of a series of re sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its apex showing a structure that characterizes them as Kolmogorov (K-) systems. It seems not only reasonable, but also inevitable to use classical ergodic theory as a guide in the study of ergodic behaviours of quantum systems. The question is which kind of random behaviours quantum systems can exhibit and whether there is any way of classifying them. Asymptotic statistical independence and, correspondingly, complete lack of control over the distant future are typical features of classical K-systems. These properties are fully characterized by the dynamical entropy of Kolmogorov and Sinai, so that the introduction of a similar concept for quantum systems has provided the opportunity of raising meaningful questions and of proposing some non-trivial answers to them. Since in the following we shall be mainly concerned with infinite quantum systems, the algebraic approach to quantum theory will provide us with the necessary analytical tools which can be used in the commutative context, too.
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Recent Developments in Infinite Dimensional Analysis and Quantum Probability

2012-12-06

Benatti, F: Deterministic Chaos in Infinite Quantum Systems, Trieste Notes in Phys., Springer, New York, 1993. 9. Billingsley, P: Ergodic Theory and Information, Wiley, NewYork, 1965. 10. Connes, A., Narnhofer, H. and Thirring, W.; ...

Author: Luigi Accardi

Publisher: Springer Science & Business Media

ISBN: 9789401008426

Category: Mathematics

Page: 464

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Recent Developments in Infinite-Dimensional Analysis and Quantum Probability is dedicated to Professor Takeyuki Hida on the occasion of his 70th birthday. The book is more than a collection of articles. In fact, in it the reader will find a consistent editorial work, devoted to attempting to obtain a unitary picture from the different contributions and to give a comprehensive account of important recent developments in contemporary white noise analysis and some of its applications. For this reason, not only the latest results, but also motivations, explanations and connections with previous work have been included. The wealth of applications, from number theory to signal processing, from optimal filtering to information theory, from the statistics of stationary flows to quantum cable equations, show the power of white noise analysis as a tool. Beyond these, the authors emphasize its connections with practically all branches of contemporary probability, including stochastic geometry, the structure theory of stationary Gaussian processes, Neumann boundary value problems, and large deviations.
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Quantum Information and Complexity

2004

F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer (1993). * An Introduction to Chaotic dynamical Systems, Benjamin G. Casati and B. Chirikov, Quantum Chaos: Between Order and Disorder, Cambridge University Press ...

Author: Takeyuki Hida

Publisher: World Scientific

ISBN: 9789812560476

Category: Science

Page: 469

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"The Winter School and the International Conference on 'Quantum Information and Complexity' was held from 6 to 10 January 2003, at Meijo University, Nagoya"--P. v.
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Open Systems and Measurement in Relativistic Quantum Theory

1999-06-21

F. Benatti , Deterministic Chaos in Infinite Quantum Systems , ( Springer , Berlin , 1993 ) . 26. D. Voiculescu , Dynamical approximation entropies and topological entropy in operator algebras . Commun .

Author: Heinz-Peter Breuer

Publisher: Springer Science & Business Media

ISBN: 3540659781

Category: Science

Page: 256

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This book treats modern aspects of open systems, measurement, and decoherence in relativistic quantum theory. It starts with a comprehensive introduction to the problems related to measuring local and nonlocal observables and the constraints imposed by the causality principle. In the articles that follow, the emphasis lies on new theoretical models. Quantum dynamical semigroups and stochastic processes in Hilbert space are introduced, as are dynamical reduction models. Further topics include relativistic generalizations of the continuous spontaneous localization model and of the quantum state diffusion model and decoherence and the dynamical selection of preferred basis sets in the framework of continuous measurement theory and of the decoherent histories approach. Mathematical aspects of quantum measurement theory and dynamical entropies are also studied from the viewpoint of the operational approach to quantum mechanics.
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Open Quantum Systems I

2006-08-18

Benatti, F.: Deterministic Chaos in Infinite Quantum Systems. Springer, Berlin, 1993. 10. Birkhoff, G.D.: Proof of the ergodic theorem. Proc. Nat. Acad. Sci. (U.S.A.) 17 (1931), 656. Bratteli, O., Robinson, D.W.: Operator Algebras and ...

Author: Stéphane Attal

Publisher: Springer

ISBN: 9783540339229

Category: Mathematics

Page: 329

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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. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.
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Classical Nonintegrability Quantum Chaos

2012-12-06

Bibliography [1] Abraham, R., Marsden, J.E.: Foundations of Mechanics. Reading: Benjamin/Cummings; 2.Ed. 1978 [2] Benatti, F.: Deterministic Chaos in Infinite Quantum Systems. Trieste Notes in Physics. Berlin: Springer 1993 [3] Berry, ...

Author: Andreas Knauf

Publisher: Birkhäuser

ISBN: 9783034889322

Category: Science

Page: 102

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Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.
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Dynamics Information and Complexity in Quantum Systems

2009-04-17

Eds.: Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, Springer Tracts in Mod. ... F. Benatti: Deterministic Chaos in Infinite Quantum Systems, (Trieste Notes in Physics, Springer Heidelberg 1993) 23.

Author: Fabio Benatti

Publisher: Springer Science & Business Media

ISBN: 9781402093067

Category: Computers

Page: 536

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This book offers a self-contained overview of the entropic approach to quantum dynamical systems. In it, complexity in quantum dynamics is addressed by comparison with the classical ergodic, information, and algorithmic complexity theories.
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Contributions in Mathematical Physics

2007-08-15

Physics, 32, 75-82 (1994) [11] F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer (1993) [12] A.Connes, H.Narnhofer, W.Thirring, Dynamical entropy of C*-algebras and von Neumann algebras, Commun.Math.

Author: S. Twareque Ali

Publisher: Springer

ISBN: 9789386279330

Category: Mathematics

Page: 226

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Professor Gerard G. Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. In a prolific scientific career, spanning nearly five decades, Professor Emch has been one of the creative influences in the general area of mathematical physics. The present volume is a collection of tributes, from former students, colleagues and friends of Professor Emch, on the occasion of his 70th birthday. The articles featured here are a small yet representative sample of the breadth and reach of some of the ideas from mathematical physics.It is also a testimony to the impact that Professor Emch's work has had on several generations of mathematical physicists as well as to the diversity of mathematical methods used to understand them.
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Time Temporality Now

2012-12-06

Benatti F. (1993): Deterministic Chaos in Infinite Quantum Systems (Springer, Berlin). Cornfeld I.P., Fomin S.V., and Sinai Ya.G. (1982): Ergodic Theory (Springer, Berlin). Costa de Beauregard O. (1987): Time, the Physical Magnitude ...

Author: Harald Atmanspacher

Publisher: Springer Science & Business Media

ISBN: 9783642607073

Category: Science

Page: 396

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The essays in this topical volume inquire into one of the most fundamental issues of philosophy and of the cognitive and natural sciences: the riddle of time. The central feature is the tension between the experience and the conceptualization of time, reflecting an apparently unavoidable antinomy of subjective first-person accounts and objective traditional science. Is time based in the physics of inanimate matter, or does it originate in the operation of our minds? Is it essential for the constitution of reality, or is it just an illusion? Issues of time, temporality, and nowness are paradigms for interdisciplinary work in many contemporary fields of research. The authors of this volume discuss profoundly the mutual relationships and inspiring perspectives. They address a general audience.
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Quantum Bio informatics

2008

From Quantum Information to Bio-informatics : Tokyo University of Science, Japan, 14-17 March 2007 Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya ... F. Benatti, Deterministic Chaos in Infinite Quantum Systems, Springer (1993) 15.

Author: Luigi Accardi

Publisher: World Scientific

ISBN: 9789812793164

Category: Science

Page: 469

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The purpose of this volume is examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized.
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