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Quantum chaos : a new paradigm of nonlinear dynamics

Author: Katsuhiro Nakamura
Publisher: New York, NY, USA : Cambridge University Press, 1993.
Series: Cambridge nonlinear science series, 3.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
Almost all the many recent studies on chaos have been concerned with classical systems. This book, however, is one of the first to deal with quantum chaos, the natural progression from such classical systems. In this book the author deals with three major issues in quantum chaos. First, quantum mechanics is applied to both bounded and open systems exhibiting classical chaos. Potential problems involving quantum  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Katsuhiro Nakamura
ISBN: 0521392497 9780521392495
OCLC Number: 25410338
Description: xii, 208 pages : illustrations ; 24 cm.
Contents: 1. What are the problems? 1.2. Adiabatic invariants in the history of quantum mechanics. 1.3. Semiclassical quantization: Einstein, Brillouin and Keller versus Gutzwiller. 1.4. Avoided level crossing and quantum adiabatic phase. 1.5. Quantum dynamics: ergodicity, recurrence and cross-over time. 1.6. Chaos versus extrinsic disorder: application to solid-state physics --
2. Quantum billiards: from closed to open systems. 2.1. Diamagnetism of a Fermi gas: revival of Van Leeuwen's thought. 2.2. Classical dynamics in magnetic billiards. 2.3. Avoided level crossings and diamagnetism. 2.4. Open stadium billiards and quantum transport --
3. Quantum chaos in spin systems. 3.1. Quantum chaos in an antiferromagnetic spin cluster: introduction. 3.2. Classical treatment. 3.3. Quantum treatment: construction of matrix elements. 3.4. Irregular energy spectra. 3.5. New speculations. 3.6. Quantum dynamics of a pulsed spin system: discrete map and classical result. 3.7. Quantum-mechanical treatment. 3.8. Quasi-eigenstates and fractals. 3.9. Anomalous diffusion and multifractals --
4. Nonlinear dynamics in spin-wave instabilities: chaos of macroscopic quanta. 4.1. Historical problems. 4.2. Experimental evidence of chaos in yttrium iron garnet (YIG). 4.3. Quantum theory of nonlinear spin-wave dynamics. 4.4. Strange attractors and multifractals --
5. Universal dynamical system behind quantum chaos: a single-parameter case. 5.1. A remarkable bridging between quantum chaos and non-linear dynamics. 5.2. Generalized Calogero-Moser system. 5.3. Generalized Sutherland system. 5.4. Solitons and moving avoided crossings. 5.5. Statistical mechanics of generalized Calogero-Moser system. 5.6. Soliton-gas picture for quantum irregular spectra --
6. Nonadiabatic generalization, field-theoretical model and future prospects. 6.1. Nonadiabatic transitions at avoided level crossings. 6.2. Reduction to a field-theoretical model. 6.3. Future prospects.
Series Title: Cambridge nonlinear science series, 3.
Responsibility: Katsuhiro Nakamura.
More information:

Abstract:

Almost all the many recent studies on chaos have been concerned with classical systems. This book, however, is one of the first to deal with quantum chaos, the natural progression from such classical systems. In this book the author deals with three major issues in quantum chaos. First, quantum mechanics is applied to both bounded and open systems exhibiting classical chaos. Potential problems involving quantum chaos are revealed in diverse areas of solid-state science, and standard concepts, such as diamagnetism, antiferromagnetism, spin waves, electrical conductance and so on, are shown in a new light through quantum chaos. Second, adiabatic-ansatz eigenvalue problems are shown to yield a new paradigm of non linear dynamics, closing the gap between the greatly different theories of solitons and random matrices. Finally, the author provides a clue to how quantum mechanics may be improved so as to accommodate temporal chaos. This up-to-date book will be of value to researchers and graduate students in physics and mathematics studying chaos, nonlinear dynamics, quantum mechanics and solid-state science.

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