Quantum Signatures of Chaos
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Beschreibung
This textbook provides an excellent introduction to a new and rapidly developing field of research. The topics treated include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish regular and irregular motion, antiunitary symmetries (generalized time reversal) and a thorough account of the quantum mechanics of dissipative systems. Each chapter is accompanied by a selection of problems which will help the student to test and deepen his/her understanding and to acquire an active command of the methods.
The second edition is significantly expanded. Of the considerable theoretical progress lately achieved, the book focusses on the deeper statistical exploitation of level dynamics, improved control of semiclassical periodic-orbit expansions, and superanalytic techniques for dealing with various types of random matrices.
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.
This book is 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
Chaos in quantum mechanical systems is currently a very active area of research. This introductory level textbook presents a detailed treatment of the most important phenomena and mathematical methods. Each chapter is accompanied by a selection of problems which will help the student to assimilate the material and acquire an active command of the methods.
Autor*in
Fritz Haake
Themen in »Quantum Signatures of Chaos«
classical Hamiltonian chaos dissipative systems level dynamics linear optimization nonlinear dynamics quantum chaos quantum localization quantum mechanics quantum time evolution random matrices universal spectral fluctuations
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"The book can be recommended both as a textbook and a review of the subject. The rich set of references allows one to catch up with the current literature. Exercises facilitate the study and will be of use to the lecturer. It can be a base of a solid graduate theoretical course in quantum chaos." (Pure and Applied Geophysics, 160, 2003)
"In summary, this is definitely an essential reference book for the specialist. It will also ably serve someone entering the field for the first time who needs to learn the theoretical state of the art in detail." (G. Summy (University of Oxford), Contemporary Physics 2002, vol. 43, page 232)
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