Deterministic Chaos In Infinite Quantum Systems

Author : Fabio Benatti
Publisher : Springer Science & Business Media
ISBN 13 : 3642849997
Total Pages : 229 pages
Book Rating : 4.92/5 ( download)

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Download or read book Deterministic Chaos in Infinite Quantum Systems written by Fabio Benatti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Heinz Georg Schuster
Publisher : Jacaranda
ISBN 13 :
Total Pages : 304 pages
Book Rating : 4.17/5 ( download)

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Download or read book Deterministic Chaos written by Heinz Georg Schuster and published by Jacaranda. This book was released on 1988 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Linda Reichl
Publisher : Springer Nature
ISBN 13 : 3030635341
Total Pages : 555 pages
Book Rating : 4.43/5 ( download)

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Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Nature. This book was released on 2021-04-12 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on courses given at the universities of Texas and California, this book treats an active field of research that touches upon the foundations of physics and chemistry. It presents, in as simple a manner as possible, the basic mechanisms that determine the dynamical evolution of both classical and quantum systems in sufficient generality to include quantum phenomena. The book begins with a discussion of Noether's theorem, integrability, KAM theory, and a definition of chaotic behavior; continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and concludes by showing how to apply the ideas to stochastic systems. The presentation is complete and self-contained; appendices provide much of the needed mathematical background, and there are extensive references to the current literature; while problems at the ends of chapters help students clarify their understanding. This new edition has an updated presentation throughout, and a new chapter on open quantum systems.

Author : Takeyuki Hida
Publisher : World Scientific
ISBN 13 : 9812560475
Total Pages : 469 pages
Book Rating : 4.76/5 ( download)

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Download or read book Quantum Information and Complexity written by Takeyuki Hida and published by World Scientific. This book was released on 2004 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Author : Stéphane Attal
Publisher : Springer
ISBN 13 : 3540339221
Total Pages : 347 pages
Book Rating : 4.29/5 ( download)

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Download or read book Open Quantum Systems I written by Stéphane Attal and published by Springer. This book was released on 2006-08-18 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Luigi Accardi
Publisher : Springer Science & Business Media
ISBN 13 : 9401008426
Total Pages : 455 pages
Book Rating : 4.26/5 ( download)

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Download or read book Recent Developments in Infinite-Dimensional Analysis and Quantum Probability written by Luigi Accardi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Heinz-Peter Breuer
Publisher : Springer Science & Business Media
ISBN 13 : 9783540659785
Total Pages : 256 pages
Book Rating : 4.81/5 ( download)

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Download or read book Open Systems and Measurement in Relativistic Quantum Theory written by Heinz-Peter Breuer and published by Springer Science & Business Media. This book was released on 1999-06-21 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Andreas Knauf
Publisher : Birkhäuser
ISBN 13 : 3034889321
Total Pages : 104 pages
Book Rating : 4.22/5 ( download)

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Download or read book Classical Nonintegrability, Quantum Chaos written by Andreas Knauf and published by Birkhäuser. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : E. Roy Pike
Publisher : CRC Press
ISBN 13 : 1000112101
Total Pages : 264 pages
Book Rating : 4.08/5 ( download)

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Download or read book Chaos, Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Author : Harald Atmanspacher
Publisher : Springer Science & Business Media
ISBN 13 : 3642607071
Total Pages : 393 pages
Book Rating : 4.73/5 ( download)

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Download or read book Time, Temporality, Now written by Harald Atmanspacher and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.