Conservative Systems And Quantum Chaos
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Conservative Systems And Quantum Chaos
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Author : Larry Meredith Bates
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Conservative Systems And Quantum Chaos written by Larry Meredith Bates and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This volume presents new research in classical Hamiltonian and quantum systems from the Workshop on Conservative Systems and Quantum Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in October 1992 (Waterloo, Canada). The workshop was organized so that there were presentations that formed a bridge between classical and quantum mechanical systems. Four of these papers appear in this collection, with the remaining six papers concentrating on classical Hamiltonian dynamics.
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].
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.
Cybernetical Physics
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Author : A. Fradkov
language : en
Publisher: Springer
Release Date : 2007-06-30
Cybernetical Physics written by A. Fradkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Science categories.
Cybernetical physics borrows methods from both theoretical physics and control engineering. It deals with the control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behavior or similar features that defy traditional control techniques. This book fully details this new discipline.
Nonlinear Dynamics Chaotic And Complex Systems
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Author : Eryk Infeld
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-19
Nonlinear Dynamics Chaotic And Complex Systems written by Eryk Infeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-19 with Mathematics categories.
The physics and mathematics of nonlinear dynamics, chaotic and complex systems constitute some of the most fascinating developments of late twentieth century science. It turns out that chaotic bahaviour can be understood, and even utilized, to a far greater degree than had been suspected. Surprisingly, universal constants have been discovered. The implications have changed our understanding of important phenomena in physics, biology, chemistry, economics, medicine and numerous other fields of human endeavor. In this book, two dozen scientists and mathematicians who were deeply involved in the "nonlinear revolution" cover most of the basic aspects of the field.
New Directions In Quantum Chaos
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Author : Giulio Casati
language : en
Publisher: IOS Press
Release Date : 2000
New Directions In Quantum Chaos written by Giulio Casati and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.
Nonlinear Dynamics And Quantum Chaos
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Author : Sandro Wimberger
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Nonlinear Dynamics And Quantum Chaos written by Sandro Wimberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.
The Transition To Chaos
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Author : Linda Reichl
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-13
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 2004-05-13 with Language Arts & Disciplines categories.
Based on courses given at the universities of Texas in Austin, and California in San Diego, this book deals with the basic mechanisms that determine the dynamic evolution of classical and quantum systems. 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; it continues with a detailed discussion of area-preserving maps, integrable quantum systems, spectral properties, path integrals, and periodically driven systems; and it 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. Problems at the ends of chapters help students clarify their understanding. In this new edition, the presentation will be brought up to date throughout, and a new chapter on open quantum systems will be added.
Stochasticity And Quantum Chaos
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Author : Z. Haba
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Stochasticity And Quantum Chaos written by Z. Haba 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 2013-03-07 with Science categories.
These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) as a nrst volume of a complete monograph (supposedly to be written by another person). His lectures concern the quantum mechanics of integrable systems. The quantum mechanics of non-integrable systems was the subject of the Third Max Born Symposium. It is known that classical non-integrable Hamiltonian systems show a chaotic behaviour. On the other hand quantum systems bounded in space are quasiperi odic. We believe that quantum systems have a reasonable classical limit. It is not clear how to reconcile the seemingly regular behaviour of quantum systems with the possible chaotic properties of their classical counterparts. The quantum proper ties of classically chaotic systems constitute the main subject of these Proceedings. Other topics discussed are: the quantum mechanics of dissipative systems, quantum measurement theory, the role of noise in classical and quantum systems.
Chaos In Nonlinear Oscillators
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Author : Muthusamy Lakshmanan
language : en
Publisher: World Scientific
Release Date : 1996
Chaos In Nonlinear Oscillators written by Muthusamy Lakshmanan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Science categories.
This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators are covered, together with appropriate experimental studies using nonlinear electronic circuits. Recent exciting developments in chaos research are also discussed, such as the control and synchronization of chaos and possible technological applications.