Transition To Chaos In Classical And Quantum Mechanics
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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.
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.
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.
Transition To Chaos In Classical And Quantum Mechanics
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Author : Sandro Graffi
language : en
Publisher:
Release Date : 2014-01-15
Transition To Chaos In Classical And Quantum Mechanics written by Sandro Graffi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Transition To Chaos In Classical And Quantum Mechanics
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Author : Jean Bellissard
language : en
Publisher:
Release Date : 1994
Transition To Chaos In Classical And Quantum Mechanics written by Jean Bellissard 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.
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 Schrdinger 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.
Coherent Dynamics Of Complex Quantum Systems
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Author : Vladimir M. Akulin
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-21
Coherent Dynamics Of Complex Quantum Systems written by Vladimir M. Akulin 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 2005-12-21 with Science categories.
A large number of modern problems in physics, chemistry, and quantum electronics require a consideration of population dynamics in complex multilevel quantum systems. The purpose of this book is to provide a systematic treatment of these questions and to present a number of exactly solvable problems. It considers the different dynamical problems frequently encountered in different areas of physics from the same perspective, based mainly on the fundamental ideas of group theory and on the idea of ensemble average. Also treated are concepts of complete quantum control and correction of decoherence induced errors that are complementary to the idea of ensemble average. Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.
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 Theory
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Author : Kais A. M. Al Naimee
language : en
Publisher: BoD – Books on Demand
Release Date : 2018-03-28
Chaos Theory written by Kais A. M. Al Naimee and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-28 with Computers categories.
With a good background in nonlinear dynamics, chaos theory, and applications, the author of this leading book gives a systematic treatment of the basic principle of nonlinear dynamics in different fields. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of background on chaos theory and applications in different sciences. In addition, they show overlap with the traditional field of control theory in scientific community.
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.