Classical Nonintegrability Quantum Chaos

Author : Andreas Knauf,Yakov G. Sinai
Publisher : Birkhäuser
Page : 104 pages
File Size : 52,8 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 : Andreas Knauf
Publisher : Unknown
Page : 107 pages
File Size : 45,6 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:257805262

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Classical Nonintegrability, Quantum Chaos by Andreas Knauf Pdf

Author : Katsuhiro Nakamura
Publisher : CUP Archive
Page : 228 pages
File Size : 53,5 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 : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 53,7 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 : Daniel Braun
Publisher : Springer
Page : 134 pages
File Size : 48,6 Mb
Release : 2003-07-01
Category : Science
ISBN : 9783540409168

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Dissipative Quantum Chaos and Decoherence by Daniel Braun Pdf

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.

Author : Linda Reichl
Publisher : Springer Nature
Page : 555 pages
File Size : 50,7 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 : Linda Reichl
Publisher : Springer Science & Business Media
Page : 692 pages
File Size : 47,5 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 : Da-hsuan Feng,Bailin Hao,Jian-min Yuan
Publisher : World Scientific
Page : 562 pages
File Size : 54,7 Mb
Release : 1992-09-30
Category : Electronic
ISBN : 9789814635684

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Quantum Non-integrability by Da-hsuan Feng,Bailin Hao,Jian-min Yuan Pdf

Recent developments in nonlinear dynamics has significantly altered our basic understanding of the foundations of classical physics. However, it is quantum mechanics, not classical mechanics, which describes the motion of the nucleons, atoms, and molecules in the microscopic world. What are then the quantum signatures of the ubiquitous chaotic behavior observed in classical physics? In answering this question one cannot avoid probing the deepest foundations connecting classical and quantum mechanics. This monograph reviews some of the most current thinkings and developments in this exciting field of physics.

Author : Linda Reichl
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 43,8 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 : Larry Meredith Bates,David Lawrence Rod
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 50,7 Mb
Release : 1996
Category : Science
ISBN : 9780821802540

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Conservative Systems and Quantum Chaos by Larry Meredith Bates,David Lawrence Rod Pdf

This volume presents new research in classical Hamiltonian and quantum systems from the Workshop on Conservative Systems and Quantum Chaos held during The Fields Institute Program Year on Dynamical Systems and Bifurcation Theory in October 1992 (Waterloo, Canada). The workshop was organized so that there were presentations that formed a bridge between classical and quantum mechanical systems. Four of these papers appear in this collection, with the remaining six papers concentrating on classical Hamiltonian dynamics.

Author : Giulio Casati,Boris Chirikov
Publisher : Cambridge University Press
Page : 703 pages
File Size : 55,5 Mb
Release : 1995-04-27
Category : Mathematics
ISBN : 9780521432917

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Quantum Chaos by Giulio Casati,Boris Chirikov Pdf

This book provides a comprehensive overview of our understanding of chaotic behaviour in quantum systems.

Author : Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 53,6 Mb
Release : 2008-10-04
Category : Science
ISBN : 9783540484158

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Crossover-Time in Quantum Boson and Spin Systems by Gennady P. Berman,Evgeny N. Bulgakov,Darryl D. Holm Pdf

The authors compare classical and quantum dynamics in the quasiclassical region of parameters and under the condition of unstable (chaotic) classical behavior. They estimate the characteristic time-scale at which classical and quantum solutions start to differ significantly. The method is based on exact equations for time-dependent expectation values in boson and spin coherent states, and applies to rather general Hamiltonians with many degrees of freedom. The authors develop a consistent dynamical theory for quantum nonintegrable Hamiltonians and provide explicit examples of classical-quantum "crossover-time", a very common and fundamental phenomenon in quantum nonintegrable systems. This book can be recommended to graduate students and to specialists.

Author : Z. Haba,Wojciech Cegla,Lech Jakóbczyk
Publisher : Springer Science & Business Media
Page : 222 pages
File Size : 53,5 Mb
Release : 2013-03-07
Category : Science
ISBN : 9789401101691

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Stochasticity and Quantum Chaos by Z. Haba,Wojciech Cegla,Lech Jakóbczyk Pdf

These are the proceedings of the Third Max Born Symposium which took place at SobOtka Castle in September 1993. The Symposium is organized annually by the Institute of Theoretical Physics of the University of Wroclaw. Max Born was a student and later on an assistant at the University of Wroclaw (Wroclaw belonged to Germany at this time and was called Breslau). The topic of the Max Born Sympo sium varies each year reflecting the developement of theoretical physics. The subject of this Symposium "Stochasticity and quantum chaos" may well be considered as a continuation of the research interest of Max Born. Recall that Born treats his "Lectures on the mechanics of the atom" (published in 1925) as a nrst volume of a complete monograph (supposedly to be written by another person). His lectures concern the quantum mechanics of integrable systems. The quantum mechanics of non-integrable systems was the subject of the Third Max Born Symposium. It is known that classical non-integrable Hamiltonian systems show a chaotic behaviour. On the other hand quantum systems bounded in space are quasiperi odic. We believe that quantum systems have a reasonable classical limit. It is not clear how to reconcile the seemingly regular behaviour of quantum systems with the possible chaotic properties of their classical counterparts. The quantum proper ties of classically chaotic systems constitute the main subject of these Proceedings. Other topics discussed are: the quantum mechanics of dissipative systems, quantum measurement theory, the role of noise in classical and quantum systems.

Author : Predrag Cvitanovic,I. Percival,A. Wirzba
Publisher : Springer
Page : 0 pages
File Size : 53,7 Mb
Release : 2010-12-15
Category : Science
ISBN : 9048141206

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Quantum Chaos — Quantum Measurement by Predrag 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 : K. Nakamura
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 40,5 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306471216

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Quantum versus Chaos by K. Nakamura Pdf

Quantum and chaos, key concepts in contemporary science, are incompatible by nature. This volume presents an investigation into quantum transport in mesoscopic or nanoscale systems which are classically chaotic and shows the success and failure of quantal, semiclassical, and random matrix theories in dealing with questions emerging from the mesoscopic cosmos. These traditional theories are critically analysed, and this leads to a new direction. To reconcile quantum with chaos and to restore genuine temporal chaos in quantum systems, a time-discrete variant of quantum dynamics is proposed. Audience:This book will be of interest to graduate students and researchers in physics, chemistry and mathematics, whose work involves fundamental questions of quantum mechanics in chaotic systems.