Author : Hans-Jürgen Stöckmann
Publisher : Cambridge University Press
Page : 386 pages
File Size : 33,76 MB
Release : 1999-10-13
Category : Science
ISBN : 0521592844
Discusses quantum chaos, an important area of nonlinear science.
Author : Martin C. Gutzwiller
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 32,90 MB
Release : 2013-11-27
Category : Mathematics
ISBN : 1461209838
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 : Fritz Haake
Publisher : Springer Science & Business Media
Page : 491 pages
File Size : 36,64 MB
Release : 2013-03-09
Category : Science
ISBN : 3662045060
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 : Sandro Wimberger
Publisher : Springer
Page : 215 pages
File Size : 33,38 MB
Release : 2014-05-13
Category : Science
ISBN : 331906343X
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 : Katsuhiro Nakamura
Publisher : CUP Archive
Page : 228 pages
File Size : 10,36 MB
Release : 1994-06-02
Category : Mathematics
ISBN : 9780521467469
Past studies on chaos have been concerned with classical systems but this book is one of the first to deal with quantum chaos.
Author : Linda Reichl
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 36,69 MB
Release : 2013-04-17
Category : Science
ISBN : 1475743521
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 : Victor J. Stenger
Publisher : Prometheus Books
Page : 292 pages
File Size : 47,73 MB
Release : 2009-09-25
Category : Religion
ISBN : 1615920587
Stenger alternates his discussions of popular spirituality with a survey of what the findings of 20th-century physics actually mean in laypersons terms--without equations.
Author : F.Tito Arecchi
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 22,43 MB
Release : 2012-12-06
Category : Science
ISBN : 364271708X
Of the variety of nonlinear dynamical systems that exhibit deterministic chaos optical systems both lasers and passive devices provide nearly ideal systems for quantitative investigation due to their simplicity both in construction and in the mathematics that describes them. In view of their growing technical application the understanding, control and possible exploitation of sources of instability in these systems has considerable practical importance. The aim of this volume is to provide a comprehensive coverage of the current understanding of optical instabilities through a series of reviews by leading researchers in the field. The book comprises nine chapters, five on active (laser) systems and four on passive optically bistable systems. Instabilities and chaos in single- (and multi-) mode lasers with homogeneously and broadened gain media are presented and the influence of an injected signal, loss modulation and also feedback of laser output on this behaviour is treated. Both electrically excited and optically pumped gas lasers are considered, and an analysis of dynamical instabilities in the emission from free electron lasers are presented. Instabilities in passive optically bistable systems include a detailed analysis of the global bifurcations and chaos in which transverse effects are accounted for. Experimental verification of degenerative pulsations and chaos in intrinsic bistable systems is described for various optical feedback systems in which atomic and molecular gases and semiconductors are used as the nonlinear media. Results for a hybrid bistable optical system are significant in providing an important test of current understanding of the dynamical behaviour of passive bistable systems.
Author : Linda Reichl
Publisher : Springer Nature
Page : 555 pages
File Size : 33,51 MB
Release : 2021-04-12
Category : Science
ISBN : 3030635341
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 : Serwan Asaad
Publisher : Springer Nature
Page : 212 pages
File Size : 36,13 MB
Release : 2021-10-19
Category : Science
ISBN : 3030834735
Nuclear spins are highly coherent quantum objects that were featured in early ideas and demonstrations of quantum information processing. In silicon, the high-fidelity coherent control of a single phosphorus (31-P) nuclear spin I=1/2 has demonstrated record-breaking coherence times, entanglement, and weak measurements. In this thesis, we demonstrate the coherent quantum control of a single antimony (123-Sb) donor atom, whose higher nuclear spin I = 7/2 corresponds to eight nuclear spin states. However, rather than conventional nuclear magnetic resonance (NMR), we employ nuclear electric resonance (NER) to drive nuclear spin transitions using localized electric fields produced within a silicon nanoelectronic device. This method exploits an idea first proposed in 1961 but never realized experimentally with a single nucleus, nor in a non-polar crystal such as silicon. We then present a realistic proposal to construct a chaotic driven top from the nuclear spin of 123-Sb. Signatures of chaos are expected to arise for experimentally realizable parameters of the system, allowing the study of the relation between quantum decoherence and classical chaos, and the observation of dynamical tunneling. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors, hybrid spin-mechanical quantum systems, and quantum-computing elements using all-electrical controls.
