## Quantum Chaos: A New Paradigm of Nonlinear DynamicsAlmost all the many past 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 fresh 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. First published in 1993, this book will be of value to researchers and graduate students in physics and mathematics studying chaos, non-linear dynamics, quantum mechanics and solid-state science. |

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### Contents

from closed to open systems | 26 |

Quantum chaos in spin systems | 56 |

chaos | 92 |

a single | 134 |

Nonadiabatic generalization fieldtheoretical model | 174 |

197 | |

205 | |

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### Common terms and phrases

adiabatic invariants amplitude avoided crossings behavior bifurcation billiards boundary Calogero-Moser chaotic systems chapter classical chaos classical dynamics completely integrable corresponding coupling curvature degeneracy denotes derivative diamagnetic distribution eigenfunctions eigenvalue problem electron energy spectra ensemble ergodic experimental finite fixed points fluctuations fractal dimension frequency fully chaotic function gauge potential gCM system given Hamiltonian Hermitian increasing indicates irregular spectra kicked rotator Landau lattice Legendre limit linear Lyapunov exponent magnetic field magnon matrix elements Nakamura nonintegrability parameters nonlinear dynamics Note observed obtain oscillations particles periodic orbits perpendicular pumping phase space pmin Poincare section quantization quantum chaos quantum dynamics quantum mechanics quantum numbers quantum transport quasienergies quasiperiodic random matrix theory regime region resonance respectively scaling Sd billiards semiclassical semiclassical limit solid-state physics solitons spectrum spin system spin-wave modes stadium billiards strange attractor structures Suhl Suhl threshold symmetry trace formula transition values variables wave wavefunctions zero

### References to this book

Quantum versus Chaos: Questions Emerging from Mesoscopic Cosmos K. Nakamura No preview available - 1997 |

Proceedings of the International Symposium Quantum Chemistry and Technology ... Hiroshi Hasegawa No preview available - 1994 |