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Transition To Chaos In Classical And Quantum Mechanics
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Book Synopsis Chaos in Classical and Quantum Mechanics by : Martin C. Gutzwiller
Download or read book Chaos in Classical and Quantum Mechanics written by Martin C. Gutzwiller and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Transition to Chaos by : Linda Reichl
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Transition to Chaos in Classical and Quantum Mechanics by : Centro internazionale matematico estivo. Session
Download or read book Transition to Chaos in Classical and Quantum Mechanics written by Centro internazionale matematico estivo. Session and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Transition to Chaos by : Linda Reichl
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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].
Book Synopsis Transition to Chaos in Classical and Quantum Mechanics by : Sandro Graffi
Download or read book Transition to Chaos in Classical and Quantum Mechanics written by Sandro Graffi and published by Springer. This book was released on 2006-11-15 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Transition to Chaos by : Linda Reichl
Download or read book The Transition to Chaos written by Linda Reichl and published by Springer Nature. This book was released on 2021-04-12 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Transition to Chaos in Classical and Quantum Mechanics by : Sandro Graffi
Download or read book Transition to Chaos in Classical and Quantum Mechanics written by Sandro Graffi and published by . This book was released on 2014-01-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Order, Chaos, Order by : Philip Stehle
Download or read book Order, Chaos, Order written by Philip Stehle and published by Oxford University Press, USA. This book was released on 1994 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Transition to Chaos in Classical and Quantum Mechanics by : Jean Bellissard
Download or read book Transition to Chaos in Classical and Quantum Mechanics written by Jean Bellissard and published by . This book was released on 1994 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classical Nonintegrability, Quantum Chaos by : Andreas Knauf
Download or read book Classical Nonintegrability, Quantum Chaos written by Andreas Knauf and published by Birkhäuser. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.
Book Synopsis Quantum Chaos by : Hans-Jürgen Stöckmann
Download or read book Quantum Chaos written by Hans-Jürgen Stöckmann and published by Cambridge University Press. This book was released on 1999-10-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses quantum chaos, an important area of nonlinear science.
Book Synopsis The Physics of Phase Space by : Young S. Kim
Download or read book The Physics of Phase Space written by Young S. Kim and published by Springer. This book was released on 2005-09-13 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Chaos in Atomic Physics by : R. Blümel
Download or read book Chaos in Atomic Physics written by R. Blümel and published by Cambridge University Press. This book was released on 1997-07-24 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent introduction to the manifestations of chaos in atoms and molecules.
Book Synopsis Dissipative Quantum Chaos and Decoherence by : Daniel Braun
Download or read book Dissipative Quantum Chaos and Decoherence written by Daniel Braun and published by Springer. This book was released on 2003-07-01 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This overview of the state of the art of research in an exciting field mainly emphasizes the development of a semiclassical formalism that allows one to incorporate the effect of dissipation and decoherence in a precise, yet tractable way into the quantum mechanics of classically chaotic systems.
Book Synopsis Quantum Mechanics, Diffusion and Chaotic Fractals by : Mohammed S. El Naschie
Download or read book Quantum Mechanics, Diffusion and Chaotic Fractals written by Mohammed S. El Naschie and published by Pergamon. This book was released on 1995 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophical and analytical silhouette of quantum mechanics can only take shape against a background of classical mechanics. As classical mechanics has undergone a radical reappraisal with the discovery of deterministic chaos and fractals, then quantum mechanics must be looked at again from the viewpoint of nonlinear dynamics. This book does just that, not solely from the point of view of quantum chaos, but also by looking at the hidden chaotic roots of quantum mechanics. Several of the contributions included in the book are concerned with the geometrization of physics and its consequences for quantum mechanics. Besides the main theme of the book, other equally interesting interpretations are represented, including the cellular automaton version of quantum mechanics and a radical endophysical interpretation: another contribution looks at the possibility of chaos in Einstein's fundamental equations. Some of the papers presented here are destined to be the subject of debate, agreement and passionate disagreement for some time.
Book Synopsis Quantum Chaos by : Katsuhiro Nakamura
Download or read book Quantum Chaos written by Katsuhiro Nakamura and published by CUP Archive. This book was released on 1994-06-02 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.
Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz
Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
