Transition To Chaos In Classical And Quantum Mechanics
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The Transition to Chaos
Author | : Linda Reichl |
Publsiher | : Springer Science & Business Media |
Total Pages | : 692 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 9781475743500 |
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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.
Transition to Chaos in Classical and Quantum Mechanics
![Transition to Chaos in Classical and Quantum Mechanics](https://youbookinc.com/wp-content/uploads/2024/06/cover.jpg)
Author | : Centro internazionale matematico estivo. Session |
Publsiher | : Unknown |
Total Pages | : 0 |
Release | : 1994 |
Genre | : Chaotic behavior in systems |
ISBN | : OCLC:1132028930 |
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Chaos in Classical and Quantum Mechanics
Author | : Martin C. Gutzwiller |
Publsiher | : Springer Science & Business Media |
Total Pages | : 445 |
Release | : 2013-11-27 |
Genre | : Mathematics |
ISBN | : 9781461209836 |
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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.
The Transition to Chaos
Author | : Linda Reichl |
Publsiher | : Springer Science & Business Media |
Total Pages | : 566 |
Release | : 2013-04-17 |
Genre | : Science |
ISBN | : 9781475743524 |
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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].
Transition to Chaos in Classical and Quantum Mechanics
Author | : Sandro Graffi |
Publsiher | : Springer |
Total Pages | : 197 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 9783540487821 |
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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.
The Transition to Chaos
Author | : Linda Reichl |
Publsiher | : Springer Nature |
Total Pages | : 555 |
Release | : 2021-04-12 |
Genre | : Science |
ISBN | : 9783030635343 |
Download The Transition to Chaos Book in PDF, Epub and Kindle
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.
Transition to Chaos in Classical and Quantum Mechanics
Author | : Sandro Graffi |
Publsiher | : Unknown |
Total Pages | : 204 |
Release | : 2014-01-15 |
Genre | : Electronic Book |
ISBN | : 3662164779 |
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Order Chaos Order
Author | : Philip Stehle |
Publsiher | : Oxford University Press, USA |
Total Pages | : 352 |
Release | : 1994 |
Genre | : Language Arts & Disciplines |
ISBN | : UOM:39015026859382 |
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Explores the confusion among physicists at the beginning of the 20th century when experimental findings kept not fitting into their mechanical view of the universe, the theoretical speculations and experimental innovations they responded with, and the new science that emerged. The mathematical details are set apart in boxes to allow nontechnical readers to engage the flow of the narrative uninterrupted. Paper edition (unseen), $29.95. Annotation copyright by Book News, Inc., Portland, OR