Quantum Chaos
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| Author | : Martin C. Gutzwiller |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 445 |
| Release | : 2013-11-27 |
| Genre | : 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 | : Hans-Jürgen Stöckmann |
| Publisher | : Cambridge University Press |
| Total Pages | : 386 |
| Release | : 1999-10-13 |
| Genre | : Science |
| ISBN | : 0521592844 |
Discusses quantum chaos, an important area of nonlinear science.
| Author | : Fritz Haake |
| Publisher | : Springer |
| Total Pages | : 659 |
| Release | : 2019-02-18 |
| Genre | : Science |
| ISBN | : 3319975803 |
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 |
| Total Pages | : 215 |
| Release | : 2014-05-13 |
| Genre | : 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 | : Linda Reichl |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 566 |
| Release | : 2013-04-17 |
| Genre | : 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 | : Katsuhiro Nakamura |
| Publisher | : CUP Archive |
| Total Pages | : 228 |
| Release | : 1994-06-02 |
| Genre | : 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 | : Giulio Casati |
| Publisher | : Cambridge University Press |
| Total Pages | : 700 |
| Release | : 1995-04-27 |
| Genre | : Science |
| ISBN | : 9780521432917 |
This book represents a comprehensive overview of our present understanding of chaotic behavior in a wide variety of quantum and semiclassical systems, and describes both experimental and theoretical investigations. A general introduction sets out the main features of chaos in quantum systems. Thereafter, in an authoritative collection of new or previously published papers, prominent scientists put forward their particular interpretations of quantum chaos with reference to a broad range of interesting physical systems.
| Author | : F.Tito Arecchi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 260 |
| Release | : 2012-12-06 |
| Genre | : 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 |
| Total Pages | : 555 |
| Release | : 2021-04-12 |
| Genre | : 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 | : Katsuhiro Nakamura |
| Publisher | : |
| Total Pages | : 228 |
| Release | : 2004 |
| Genre | : Mesoscopic phenomena (Physics). |
| ISBN | : 9780198525899 |
Dynamics of billiard balls and their role in physics have received wide attention since the monumental lecture by Lord Kelvin at the turn of the 19th century. 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 itsexploration 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 interpretquantum 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 fiveto 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.
