Deterministic Chaos in Infinite Quantum Systems PDF Download
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Author: Fabio Benatti
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 272
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Book Description
Author: Fabio Benatti
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 272
Get Book Here
Book Description
Author: Fabio Benatti
Publisher: Springer Science & Business Media
ISBN: 3642849997
Category : Science
Languages : en
Pages : 229
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Book Description
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: Wiley-VCH
ISBN:
Category : Science
Languages : en
Pages : 328
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Book Description
This is the revised and updated 3rd edition of this highly regarded textbook. A new chapter on controlling chaos has been added. Translations into Japanese, Chinese, German, Russian and Polish demonstrate the international interest in this book. From reviews of former editions: In this book, Schuster gives a very useful summary of the main ideas of the subject as it now stands. Although a physist by training and style, he organizes his treatment by the logic of the mathematics, which is based on the concept of a dynamical system. Students about to begin research into chaos, and practising scientists new to the subject, will find this book well worth reading. Nature This text sets a standard which other authors and publishers in physics should strive to meet. Physics Bulletin
Author: Bertrand Duplantier
Publisher: Springer Science & Business Media
ISBN: 3034806973
Category : Mathematics
Languages : en
Pages : 281
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Book Description
This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ζ-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ζ-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S. Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians.
Author: E. Roy Pike
Publisher: CRC Press
ISBN: 1000112101
Category : Mathematics
Languages : en
Pages : 264
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Book Description
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: Ilya Prigogine
Publisher: University Press of America
ISBN:
Category : Science
Languages : en
Pages : 152
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Book Description
The role of chaos in science and mathematics is examined in detail by the essays that comprise this work. Distinguished scholars specializing in mathematics, physics, and chemistry discuss the following subjects: Fractals, by Benoit Mandelbrot; The Causality Principle, Deterministic Laws and Chaos, by Heinz-Otto Peitgen; The Transition to Chaos, by Mitchell Feigenbaum; Time, Dynamics and Chaos: Integrating Poincare's 'Non-Integrable Systems', by Ilya Prigogine; What Is Chaos, by Steve Smale; Chaos and Cosmos: A Theological Approach, by John Polkinghorne; and Chaos and Beyond, by James Gleick. Introduction by John Holte. This volume is number 26 in the Nobel Conference Series. Co-published with the Nobel Conference.
Author: Robert Warren Valentine
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Author: P. Cvitanovic
Publisher: Springer Science & Business Media
ISBN: 9401579792
Category : Science
Languages : en
Pages : 325
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Book Description
This volume contains the proceedings of the NATO Advanced Research Workshop on `Quantum Chaos -- Theory and Experiment', held at the Niels Bohr Institute, University of Copenhagen, from 28 May to 1 June 1991. The work brings together leading quantum chaos theorists and experimentalists and greatly improves our understanding of the physics of quantum systems whose classical limit is chaotic. Quantum chaos is a subject of considerable current interest in a variety of fields, in particular nuclear physics, chemistry, statistical mechanics, atomic physics, condensed matter physics and nonlinear dynamics. The volume contains lectures about the currently most active fronts of quantum chaos, such as scars, semiclassical methods, quantum diffusion, random matrix spectra, quantum chaos in atomic and nuclear physics, and possible implications of quantum chaos for the problem of quantum measurement. Part of the book -- The Physics of Quantum Measurements -- is dedicated to the memory of John Bell.
Author: Joseph L. McCauley
Publisher: Cambridge University Press
ISBN: 1107393272
Category : Science
Languages : en
Pages : 352
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Book Description
This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the emphasis makes it very different from all other books in the field. It provides the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision cannot be avoided in computation or experiment. This leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized in computation or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed.
Author: Daniel Braun
Publisher: Springer
ISBN: 3540409165
Category : Science
Languages : en
Pages : 139
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Book Description
This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems.
