The Transition To Chaos
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The Transition To Chaos
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Author : Linda Reichl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Transition To Chaos written by Linda Reichl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
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.
The Transition To Chaos
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Author : Linda Reichl
language : en
Publisher: Springer Nature
Release Date : 2021-04-12
The Transition To Chaos written by Linda Reichl and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-12 with Science categories.
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.
The Transition To Chaos
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Author : Linda Reichl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Transition To Chaos written by Linda Reichl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
resonances. Nonlinear resonances cause divergences in conventional perturbation expansions. This occurs because nonlinear resonances cause a topological change locally in the structure of the phase space and simple perturbation theory is not adequate to deal with such topological changes. In Sect. (2.3), we introduce the concept of integrability. A sys tem is integrable if it has as many global constants of the motion as degrees of freedom. The connection between global symmetries and global constants of motion was first proven for dynamical systems by Noether [Noether 1918]. We will give a simple derivation of Noether's theorem in Sect. (2.3). As we shall see in more detail in Chapter 5, are whole classes of systems which are now known to be inte there grable due to methods developed for soliton physics. In Sect. (2.3), we illustrate these methods for the simple three-body Toda lattice. It is usually impossible to tell if a system is integrable or not just by looking at the equations of motion. The Poincare surface of section provides a very useful numerical tool for testing for integrability and will be used throughout the remainder of this book. We will illustrate the use of the Poincare surface of section for classic model of Henon and Heiles [Henon and Heiles 1964].
Chaos
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Author : Ilya Prigogine
language : en
Publisher: University Press of America
Release Date : 1993
Chaos written by Ilya Prigogine and has been published by University Press of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
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.
From Phase Transitions To Chaos
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Author : Gza Gyrgyi
language : en
Publisher: World Scientific
Release Date : 1992
From Phase Transitions To Chaos written by Gza Gyrgyi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to Pter Szpfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.
Transition To Chaos In Classical And Quantum Mechanics
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Author : Centro internazionale matematico estivo. Session
language : en
Publisher:
Release Date : 1994
Transition To Chaos In Classical And Quantum Mechanics written by Centro internazionale matematico estivo. Session and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Chaotic behavior in systems categories.
Order Chaos Order
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Author : Philip Stehle
language : en
Publisher: Oxford University Press, USA
Release Date : 1994
Order Chaos Order written by Philip Stehle and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Physics categories.
A book written for a wide audience of both students and general readers who are interested in exploring the ideas and experiments
Order In Chaos
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Author : Gavin Hamilton
language : en
Publisher:
Release Date : 2011
Order In Chaos written by Gavin Hamilton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Fluid dynamics categories.
Transition To Chaos In Classical And Quantum Mechanics
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Author : Sandro Graffi
language : en
Publisher: Springer
Release Date : 2006-11-15
Transition To Chaos In Classical And Quantum Mechanics written by Sandro Graffi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The Session was intended to give a broad survey of the mathematical problems arising in the chaotic transition of deterministic dynamical systems, both in classical and quantum mechanics. The lectures of Mather and Forni thoroughly cover the area- preserving twist maps, and include an up-to-date version of the Aubry-Mather theory. The lectures of Bellissard describe the quantum aspects: classical limit, localization, spectral properties of the relevant Schrödinger operators and thus represent an exhaus- tive introduction to the mathematics of "quantum chaos". The lectures of Degli Esposti et al. reviews equidistribu- tion of unstable periodic orbits and classical limit of quantized toral symplectomorphisms.
Chaos In Classical And Quantum Mechanics
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Author : Martin C. Gutzwiller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Chaos In Classical And Quantum Mechanics written by Martin C. Gutzwiller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
Describes the chaos apparent in simple mechanical systems with the goal of elucidating the connections between classical and quantum mechanics. It develops the relevant ideas of the last two decades via geometric intuition rather than algebraic manipulation. The historical and cultural background against which these scientific developments have occurred is depicted, and realistic examples are discussed in detail. This book enables entry-level graduate students to tackle fresh problems in this rich field.