Chaos in Classical and Quantum Mechanics PDF Download
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Author: Martin C. Gutzwiller
Publisher: Springer Science & Business Media
ISBN: 1461209838
Category : Mathematics
Languages : en
Pages : 445
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Book Description
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.
Author: Martin C. Gutzwiller
Publisher: Springer Science & Business Media
ISBN: 1461209838
Category : Mathematics
Languages : en
Pages : 445
Get Book Here
Book Description
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.
Author: Linda Reichl
Publisher: Springer Science & Business Media
ISBN: 1475743521
Category : Science
Languages : en
Pages : 566
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Book Description
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].
Author: Linda Reichl
Publisher: Springer Nature
ISBN: 3030635341
Category : Science
Languages : en
Pages : 556
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Book Description
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.
Author: Philip Stehle
Publisher: Oxford University Press, USA
ISBN:
Category : Language Arts & Disciplines
Languages : en
Pages : 446
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Book Description
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
Author: Hans-Jürgen Stöckmann
Publisher: Cambridge University Press
ISBN: 0521592844
Category : Science
Languages : en
Pages : 386
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Book Description
Discusses quantum chaos, an important area of nonlinear science.
Author: Centro internazionale matematico estivo. Session
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 0
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Book Description
Author: R. Blümel
Publisher: Cambridge University Press
ISBN: 9780521455022
Category : Science
Languages : en
Pages : 356
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Book Description
This book provides a coherent introduction to the manifestations of chaos in atoms and molecules.
Author: Young S. Kim
Publisher: Springer
ISBN: 3540479015
Category : Science
Languages : en
Pages : 457
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Book Description
The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.
Author: David D. Nolte
Publisher: Oxford University Press
ISBN: 0192528505
Category : Science
Languages : en
Pages : 348
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Book Description
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once -- setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
