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Chaotic Dynamics And Transport In Classical And Quantum Systems
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Book Synopsis Chaotic Dynamics and Transport in Classical and Quantum Systems by : Pierre Collet
Download or read book Chaotic Dynamics and Transport in Classical and Quantum Systems written by Pierre Collet and published by Kluwer Academic Pub. This book was released on 2005-03-04 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern updated review on the most important activities in today dynamical systems and statistical mechanics by some of the best experts in the domain. It gives a contemporary and pedagogical view on theories of classical and quantum chaos and complexity in hamiltonian and ergodic systems and their applications to anomalous transport in fluids, plasmas, oceans and atom-optic devices and to control of chaotic transport. The book is issued from lecture notes of the International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems" held in Cargèse (Corsica) 18th to the 30th August 2003. It reflects the spirit of the School to provide lectures at the post-doctoral level on basic concepts and tools. The first part concerns ergodicity and mixing, complexity and entropy functions, SRB measures, fractal dimensions and bifurcations in hamiltonian systems. Then, models of dynamical evolutions of transport processes in classical and quantum systems have been largely explained. The second part concerns transport in fluids, plasmas and reacting media. On the other hand, new experiments of cold optically trapped atoms and electrodynamics cavity have been thoroughly presented. Finally, several papers bear on synchronism and control of chaos. The target audience of the proceedings are physicists, mathematicians and all scientists involved in Chaos and Dynamical Systems Theory and their fundamental applications in Physics and in the Science of Complex and Nonlinear phenomena.
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 Chaotic Dynamics and Transport in Classical and Quantum Systems by : Pierre Collet
Download or read book Chaotic Dynamics and Transport in Classical and Quantum Systems written by Pierre Collet and published by Springer Science & Business Media. This book was released on 2005-07-28 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).
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 Chaotic Dynamics and Transport in Fluids and Plasmas by : Ilya Prigogine
Download or read book Chaotic Dynamics and Transport in Fluids and Plasmas written by Ilya Prigogine and published by Springer Science & Business Media. This book was released on 1992-10-31 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Market: Students and researchers in chaos, plasma physics, and fluid transport. This superb collection of invited papers offers an excellent overview of the current status and future trends in chaotic dynamics, plasma and fluid physics, nonlinear phenomena and chaos, and transport and turbulence studies.
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 Quantum versus Chaos by : K. Nakamura
Download or read book Quantum versus Chaos written by K. Nakamura and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Y2K by : Karl-Fredrik Berggren
Download or read book Quantum Chaos Y2K written by Karl-Fredrik Berggren and published by World Scientific. This book was released on 2001-10-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium. Contents: After-Dinner Speech (M C Gutzwiller)Spectral Twinkling: A New Example of Singularity-Dominated Strong Fluctuations (Summary) (M Berry)Ground State Spin and Coulomb Blockade Peak Motion in Chaotic Quantum Dots (J A Folk et al.)Quantum Chaos and Transport Phenomena in Quantum Dots (A S Sachrajda)Chaos in Quantum Ratchets (H Linke et al.)Non-Universality of Chaotic Classical Dynamics: Implications for Quantum Chaos (M Wilkinson)Chaos and Interactions in Quantum Dots (Y Alhassid)Stochastic Aspects of Many-Body Systems: The Embedded Gaussian Ensembles (H A Weidenmüller)Effect of Symmetry Breaking on Statistical Distributions (G E Mitchell & J F Shriner, Jr.)Quantum Chaos and Quantum Computers (D L Shepelyansky)Disorder and Quantum Chromodynamics — Non-Linear σ Models (T Guhr & T Wilke)Correlation Between Periodic Orbits and Their Rôle in Spectral Statistics (M Sieber & K Richter)Neutron Stars and Quantum Billiards (A Bulgac & P Magierski)Tunneling and Chaos (S Tomsovic)Relaxation and Fluctuations in Quantum Chaos (G Casati)Scars and Other Weak Localization Effects in Classically Chaotic Systems (E J Heller)Classically-Forbidden Processes in Photoabsorption Spectra (J B Delos et al.)Wave Dynamical Chaos: An Experimental Approach in Billiards (A Richter)Acoustic Chaos (C Ellegaard et al.)Wave-Chaotic Optical Resonators and Lasers (A D Stone)Angular Momentum Localization in Oval Billiards (J U Nöckel)Chaos and Time-Reversed Acoustics (M Fink)and other papers Readership: Quantum, nuclear, atomic, condensed matter and high energy physicists, as well as researchers in classical wave physics. Keywords:
Book Synopsis Nonlinear Dynamics and Quantum Chaos by : Sandro Wimberger
Download or read book Nonlinear Dynamics and Quantum Chaos written by Sandro Wimberger and published by Springer Nature. This book was released on 2023-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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 134 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 Chaotic Behavior in Quantum Systems by : Giulio Casati
Download or read book Chaotic Behavior in Quantum Systems written by Giulio Casati and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Six years ago, in June 1977, the first international conference on chaos in classical dynamical systems took place here in Como. For the first time, physicists, mathematicians, biologists, chemists, economists, and others got together to discuss the relevance of the recent progress in nonlinear classical dynamics for their own research field. Immediately after, pUblication of "Nonlinear Science Abstracts" started, which, in turn, led to the Physica D Journal and to a rapid increase of the research activity in the whole area with the creation of numerous "Nonlinear Centers" around the world. During these years great progress has been made in understanding the qualitative behavior of classical dynamical systems and now we can appreciate the beautiful complexity and variety of their motion. Meanwhile, an increasing number of scientists began to wonder whether and how such beautiful structures would persist in quantum motion. Indeed, mainly integrable systems have been previously con sidered by Quantum Mechanics and therefore the problem is open how to describe the qualitative behavior of systems whose classical limit is non-integrable. The present meeting was organized in view of the fact that scientists working in different fields - mathematicians, theoretical physicists, solid state physicists, nuclear physicists, chemists and others - had common problems. Moreover, we felt that it was necessary to clarify some fundamental questions concerning the logical basis for the discussion including the very definition of chaos in Quantum Mechanics.
Book Synopsis Irregular Atomic Systems and Quantum Chaos by : Jean-Claude Gay
Download or read book Irregular Atomic Systems and Quantum Chaos written by Jean-Claude Gay and published by CRC Press. This book was released on 1992 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the study of irregular behavior in few-body systems, with emphasis on the aspects of atomic physics. Areas covered include the atom in a magnetic field, microwave ionization of Rydberg atoms, and quasi-Wigner crystals in ion traps. All but one of the papers first appeared in volume 25 of the journal Comments on atomic and molecular physics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Quantum Chaos — Quantum Measurement by : P. Cvitanovic
Download or read book Quantum Chaos — Quantum Measurement written by P. Cvitanovic and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Chaos, Noise and Fractals by : E. Roy Pike
Download or read book Chaos, Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
