Quantum Chaos
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Quantum Signatures Of Chaos
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Author : Fritz Haake
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Quantum Signatures Of Chaos written by Fritz Haake and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The warm reception of the first edition, as well as the tumultuous development of the field of quantum chaos have tempted me to rewrite this book and include some of the important progress made during the past decade. Now we know that quantum signatures of chaos are paralleled by wave signa tures. Whatever is undergoing wavy space-time variations, be it sound, electro magnetism, or quantum amplitudes, each shows exactly the same manifestations of chaos. The common origin is nonseparability of the pertinent wave equation; that latter "definition" of chaos, incidentally, also applies to classical mechanics if we see the Hamilton-Jacobi equation as the limiting case of a wave equation. At any rate, drums, concert halls, oscillating quartz blocks, microwave and opti cal oscillators, electrons moving ballistically or with impurity scattering through mesoscopic devices all provide evidence and data for wave or quantum chaos. All of these systems have deep analogies with billiards, much as the latter may have appeared of no more than academic interest only a decade ago. Of course, molec ular, atomic, and nuclear spectroscopy also remain witnesses of chaos, while the chromodynamic innards of nucleons are beginning to attract interest as methods of treatment become available.
Nonlinear Dynamics And Quantum Chaos
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Author : Sandro Wimberger
language : en
Publisher: Springer
Release Date : 2014-05-13
Nonlinear Dynamics And Quantum Chaos written by Sandro Wimberger and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-13 with Science categories.
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.
Chaos In Classical And Quantum Mechanics
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Author : Martin C. Gutzwiller
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Chaos In Classical And Quantum Mechanics written by Martin C. Gutzwiller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
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
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Author : Linda Reichl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Transition To Chaos written by Linda Reichl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
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].
Nonlinear Dynamics And Quantum Chaos
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Author : Sandro Wimberger
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Nonlinear Dynamics And Quantum Chaos written by Sandro Wimberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
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. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.
Quantum Chaos And Quantum Dots
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Author : Katsuhiro Nakamura
language : en
Publisher:
Release Date : 2004
Quantum Chaos And Quantum Dots written by Katsuhiro Nakamura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
Dynamics of billiard balls and their role in physics have received wide attention. Billiards can nowadays be created as quantum dots in the microscopic world enabling one to envisage the so-called quantum chaos, (i.e.: quantum manifestation of chaos of billiard balls). In fact, owing to recent progress in advanced technology, nanoscale quantum dots, such as chaotic stadium and antidot lattices analogous to the Sinai Billiard, can be fabricated at the interface of semiconductor heterojunctions. This book begins ite exploration of the effect of chaotic electron dynamics on ballistic quantum transport in quantum dots with a puzzling experiment on resistance fluctuations for stadium and circle dots. Throughout the text, major attention is paid to the semiclassical theory which makes it possible to interpret quantum phenomena in the language of the classical world. Chapters one to four are concerned with the elementary statistical methods (curvature, Lyapunov exponent, Kolmogorov-Sinai entropy and escape rate), which are needed for a semiclassical description of transport in quantum dots. Chapters five to ten discuss the topical subjects in the field, including the ballistic weak localization, Altshuler-Aronov-Spivak oscillation, partial time-reversal symmetry, persistent current, Arnold diffusion and Coulomb blockade.
Dissipative Quantum Chaos And Decoherence
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Author : Daniel Braun
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-01-25
Dissipative Quantum Chaos And Decoherence written by Daniel Braun and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-25 with Language Arts & Disciplines categories.
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.
Quantum Chaos
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Author : Giulio Casati
language : en
Publisher: Cambridge University Press
Release Date : 1995-04-27
Quantum Chaos written by Giulio Casati and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-27 with Mathematics categories.
This book provides a comprehensive overview of our understanding of chaotic behaviour in quantum systems.
Quantum Chaos Quantum Measurement
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Author : P. Cvitanovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Quantum Chaos Quantum Measurement written by P. Cvitanovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
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.
Cybernetical Physics
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Author : A. Fradkov
language : en
Publisher: Springer
Release Date : 2007-06-30
Cybernetical Physics written by A. Fradkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Science categories.
Cybernetical physics borrows methods from both theoretical physics and control engineering. It deals with the control of complex systems is one of the most important aspects in dealing with systems exhibiting nonlinear behavior or similar features that defy traditional control techniques. This book fully details this new discipline.