Chaos In Classical And Quantum Mechanics

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 45,7 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9781461209836

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Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller Pdf

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 : Centro internazionale matematico estivo. Session
Publisher : Unknown
Page : 0 pages
File Size : 47,6 Mb
Release : 1994
Category : Chaotic behavior in systems
ISBN : OCLC:1132028930

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Transition to Chaos in Classical and Quantum Mechanics by Centro internazionale matematico estivo. Session Pdf

Author : Andreas Knauf,Yakov G. Sinai
Publisher : Birkhäuser
Page : 104 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034889322

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Classical Nonintegrability, Quantum Chaos by Andreas Knauf,Yakov G. Sinai Pdf

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.

Author : Linda Reichl
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 43,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9781475743524

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The Transition to Chaos by Linda Reichl Pdf

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 Science & Business Media
Page : 692 pages
File Size : 53,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781475743500

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The Transition to Chaos by Linda Reichl Pdf

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 : P. Cvitanovic,I. Percival,A. Wirzba
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 54,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401579797

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Quantum Chaos — Quantum Measurement by P. Cvitanovic,I. Percival,A. Wirzba Pdf

This volume contains the proceedings of the NATO Advanced Research Workshop on `Quantum Chaos -- Theory and Experiment', held at the Niels Bohr Institute, University of Copenhagen, from 28 May to 1 June 1991. The work brings together leading quantum chaos theorists and experimentalists and greatly improves our understanding of the physics of quantum systems whose classical limit is chaotic. Quantum chaos is a subject of considerable current interest in a variety of fields, in particular nuclear physics, chemistry, statistical mechanics, atomic physics, condensed matter physics and nonlinear dynamics. The volume contains lectures about the currently most active fronts of quantum chaos, such as scars, semiclassical methods, quantum diffusion, random matrix spectra, quantum chaos in atomic and nuclear physics, and possible implications of quantum chaos for the problem of quantum measurement. Part of the book -- The Physics of Quantum Measurements -- is dedicated to the memory of John Bell.

Author : Sandro Graffi
Publisher : Springer
Page : 197 pages
File Size : 55,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540487821

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Transition to Chaos in Classical and Quantum Mechanics by Sandro Graffi Pdf

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.

Author : Katsuhiro Nakamura
Publisher : CUP Archive
Page : 228 pages
File Size : 55,7 Mb
Release : 1994-06-02
Category : Mathematics
ISBN : 0521467462

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Quantum Chaos by Katsuhiro Nakamura Pdf

Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.

Author : Fritz Haake,Sven Gnutzmann,Marek Kuś
Publisher : Springer
Page : 659 pages
File Size : 46,7 Mb
Release : 2019-02-18
Category : Science
ISBN : 9783319975801

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Quantum Signatures of Chaos by Fritz Haake,Sven Gnutzmann,Marek Kuś Pdf

This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

Author : Linda Reichl
Publisher : Springer Nature
Page : 555 pages
File Size : 55,9 Mb
Release : 2021-04-12
Category : Science
ISBN : 9783030635343

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The Transition to Chaos by Linda Reichl Pdf

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 : R. Blümel,W. P. Reinhardt
Publisher : Cambridge University Press
Page : 356 pages
File Size : 43,5 Mb
Release : 1997-07-24
Category : Science
ISBN : 0521455022

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Chaos in Atomic Physics by R. Blümel,W. P. Reinhardt Pdf

This book provides a coherent introduction to the manifestations of chaos in atoms and molecules.

Author : Sandro Wimberger
Publisher : Springer
Page : 206 pages
File Size : 53,5 Mb
Release : 2014-05-13
Category : Science
ISBN : 9783319063430

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. 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. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : Hans-Jürgen Stöckmann
Publisher : Cambridge University Press
Page : 386 pages
File Size : 48,6 Mb
Release : 1999-10-13
Category : Science
ISBN : 9780521592840

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Quantum Chaos by Hans-Jürgen Stöckmann Pdf

Discusses quantum chaos, an important area of nonlinear science.

Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 42,5 Mb
Release : 1991-08-01
Category : Mathematics
ISBN : 9780387971735

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Chaos in Classical and Quantum Mechanics by Martin C. Gutzwiller Pdf

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 : Sandro Graffi
Publisher : Unknown
Page : 204 pages
File Size : 47,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662164779

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Transition to Chaos in Classical and Quantum Mechanics by Sandro Graffi Pdf