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Download or read book The Interplay of Chaos and Dissipation in Driven Quantum Systems written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Interplay of Chaos and Dissipation in Driven Quantum Systems written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Bistable quantum systems show in parameter regimes with mixed regular/chaotic dynamics a characteristic phenomenon: chaotic tunneling -- coherent transport between regular islands which are separated by a chaotic layer. In this process, quantum mechanical states which are localized in chaotic regions of phase space, serve as a bridge between regular regions. The fact that chaotic states are typically delocalized, results in enhanced tranport -- for the present case in larger tunneling rates. As the appropriate spectral feature, one finds crossings of chaotic singlets with regular (tunnel) doublets. The influence of dissipation and the related decoherence on this tunnel phenomenon is studied in this work. The harmonically driven double well potential served as a model. It turned out that chaotic tunneling is accompanyed by enhanced decoherence and that the dynamics involves by far more than two levels. In the long term limit it results in a staedy flow between all states whose mean energy is below the barrier. While the influence of the driving has been treated exactly within a Floquet formalism, it was for an efficient description of the dissipative effects neccessary to restrict ourselves to weak dissipation. The applicability of the approximations known from literatur, namely Born-Markov and rotating-wave approximation, has been investigated and a modyfied approach based on the Floquet theorem has been derived. Its quality has been studied by means of an exactly solvable model, the parameterically driven harmonic oscillator. For this model system we derived analytical solutions of the different master equations.
Author : Linda Reichl
Publisher : Springer Nature
ISBN 13 : 3030635341
Total Pages : 555 pages
Book Rating : 4.0/5 (36 download)
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.
Author : Thomas Dittrich
Publisher : Wiley-VCH
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)
Download or read book Quantum Transport and Dissipation written by Thomas Dittrich and published by Wiley-VCH. This book was released on 1998-03-04 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing emphasis and importance of mesoscopic systems for tomorrow's high-tech electronics industry as well as a growing research interest in the subject has given rise to the need for a modern introductory text at the graduate level. This book aims to provide the necessary theory and tools to carry out research into the various aspects of the subject. It starts with a chapter on the theory of quantum transport giving a survey of the basic theory used in transport phenomena including scattering, linear response theory, weak localization, conductance fluctuations and the Landauer-B?ttiker formalism. Various aspects of chaos in quantum systems as well as dissipative quantum systems are discussed. Other topics of importance such as single electron tunneling, driven bistable systems, quantized transport and electron liquids are also covered in detail. Graduate students as well as newcomers to this exciting and expanding field will find this work useful to adopt the necessary theory and overview required to go deeper into the original literature and to carry out research.
Author : Daniel Braun
Publisher : Springer
ISBN 13 : 3540409165
Total Pages : 139 pages
Book Rating : 4.5/5 (44 download)
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.
Author : Georg M. Reuther
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832528466
Total Pages : 158 pages
Book Rating : 4.8/5 (325 download)
Download or read book Decoherence and Time-Resolved Readout in Superconducting Quantum Circuits (Dekohärenz und Zeitaufgelösste Quantenmessung in Supraleitenden Schaltkreisen) written by Georg M. Reuther and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superconducting quantum circuits are promising candidates for solid-state based quantum computation. However, minimizing dissipation caused by external noise sources remains a tough challenge. Here, we present an analytic dissipative theory for a complex circuit of two resonators coupled via a flux qubit. In this 'quantum switch', the qubit acts as a tunable coupler between the resonators, which enables switching their interaction on and off. A natural application of this setup is to create entangled two-resonator states. However, it turns out that, even if the qubit has no dynamics, qubit dissipation affects the resonators to a considerable degree. For successful quantum information processing, it is desirable to demonstrate the coherence of qubit time evolution in single-shot experiments without too much backaction on the qubit. In the second part of this thesis, we present a novel scheme for a time-resolved single-run measurement of coherent qubit dynamics. For a charge qubit probed by a weak high-frequency signal, we find that the reflected outgoing signal possesses a time-dependent phase shift that is proportional to a qubit observable. A similar approach is presented for a flux qubit coupled to a resonantly driven high-frequency oscillator, which serves as a meter device for monitoring the time-resolved qubit dynamics.
Author : Linda Reichl
Publisher : Springer Science & Business Media
ISBN 13 : 1475743505
Total Pages : 692 pages
Book Rating : 4.4/5 (757 download)
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.
Author : D. Reguera
Publisher : Springer
ISBN 13 : 3540455574
Total Pages : 347 pages
Book Rating : 4.5/5 (44 download)
Download or read book Statistical and Dynamical Aspects of Mesoscopic Systems written by D. Reguera and published by Springer. This book was released on 2008-01-11 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Initially a subfield of solid state physics, the study of mesoscopic systems has evolved over the years into a vast field of research in its own right. Keeping track its rapid progress, this book provides a broad survey of the latest developments in the field. The focus is on statistics and dynamics of mesoscopic systems with special emphasis on topics like quantum chaos, localization, noise and fluctuations, mesoscopic optics and quantum transport in nanostructures. Written with nonspecialists in mind, this book will also be useful to graduate students wishing to familiarize themselves with this field of research.
Author : Carmen Vierheilig
Publisher :
ISBN 13 : 9783868450729
Total Pages : 162 pages
Book Rating : 4.4/5 (57 download)
Download or read book Interplay Between Dissipation and Driving in Nonlinear Quantum Systems written by Carmen Vierheilig and published by . This book was released on 2011 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sven Aberg
Publisher : World Scientific
ISBN 13 : 9814490431
Total Pages : 286 pages
Book Rating : 4.8/5 (144 download)
Download or read book Quantum Chaos Y2k, Proceedings Of Nobel Symposium 116 written by Sven Aberg and published by World Scientific. This book was released on 2001-10-09 with total page 286 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.
Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 981437492X
Total Pages : 587 pages
Book Rating : 4.8/5 (143 download)
Download or read book Quantum Dissipative Systems written by Ulrich Weiss and published by World Scientific. This book was released on 2012 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book OCo originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions OCo delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems. This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source."
Author : Pavel Exner
Publisher : Birkhauser
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.3/5 (91 download)
Download or read book Order, Disorder, and Chaos in Quantum Systems written by Pavel Exner and published by Birkhauser. This book was released on 1990 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Piotr Garbaczewski
Publisher : Springer Science & Business Media
ISBN 13 : 3540461221
Total Pages : 516 pages
Book Rating : 4.5/5 (44 download)
Download or read book Dynamics of Dissipation written by Piotr Garbaczewski and published by Springer Science & Business Media. This book was released on 2007-08-04 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical mechanics, environment-system coupling (decoherence) and applications of Markov semi-groups to name but a few. The book addresses not only experienced researchers in the field but also nonspecialists from related areas of research, postgraduate students wishing to enter the field and lecturers searching for advanced textbook material.
Author : E. Roy Pike
Publisher : CRC Press
ISBN 13 : 1000112101
Total Pages : 264 pages
Book Rating : 4.0/5 (1 download)
Download or read book Chaos, Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 2020-08-26 with total page 264 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.
Author : Ulrich Weiss
Publisher : World Scientific
ISBN 13 : 981445298X
Total Pages : 587 pages
Book Rating : 4.8/5 (144 download)
Download or read book Quantum Dissipative Systems (Fourth Edition) written by Ulrich Weiss and published by World Scientific. This book was released on 2012-03-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from first principles, this book introduces the fundamental concepts and methods of dissipative quantum mechanics and explores related phenomena in condensed matter systems. Major experimental achievements in cooperation with theoretical advances have brightened the field and brought it to the attention of the general community in natural sciences. Nowadays, working knowledge of dissipative quantum mechanics is an essential tool for many physicists. This book — originally published in 1990 and republished in 1999 and and 2008 as enlarged second and third editions — delves significantly deeper than ever before into the fundamental concepts, methods and applications of quantum dissipative systems.This fourth edition provides a self-contained and updated account of the quantum mechanics of open systems and offers important new material including the most recent developments. The subject matter has been expanded by about fifteen percent. Many chapters have been completely rewritten to better cater to both the needs of newcomers to the field and the requests of the advanced readership. Two chapters have been added that account for recent progress in the field. This book should be accessible to all graduate students in physics. Researchers will find this a rich and stimulating source.
Author : Yurii Bolotin
Publisher : Springer
ISBN 13 : 3319424963
Total Pages : 286 pages
Book Rating : 4.3/5 (194 download)
Download or read book Chaos: Concepts, Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
Author : Linda Reichl
Publisher : Springer Science & Business Media
ISBN 13 : 1475743521
Total Pages : 566 pages
Book Rating : 4.4/5 (757 download)
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].
