Quantum versus Chaos

1. Front Matter

   Pages i-x

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2. Genesis of Chaos and Breakdown of Quantization of Adiabatic Invariants

   Pages 1-14

3. Semiclassical Quantization of Chaos: Trace Formula

   Pages 15-30

4. Pseudo-Chaos Without Classical Counterpart in One-Dimensional Quantum Transport

   Pages 31-44

5. Chaos and Quantum Transport in Open Magnetic Billiards: from Stadium to Sinai Billiards

   Pages 45-78

6. Chaotic Scattering on Hyperbolic Billiards: Success of Semiclassical Theory

   Pages 79-101

7. Nonadiabaticity-Induced Quantum Chaos

   Pages 102-126

8. Level Dynamics and Statistical Mechanics

   Pages 127-161

9. Towards Time-Discrete Quantum Mechanics

   Pages 162-197

10. Conclusions and Prospects

    Pages 198-208

11. Back Matter

    Pages 209-214

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Quantum and chaos, key concepts in contemporary science, are incompatible by nature. This volume presents an investigation into quantum transport in mesoscopic or nanoscale systems which are classically chaotic and shows the success and failure of quantal, semiclassical, and random matrix theories in dealing with questions emerging from the mesoscopic cosmos. These traditional theories are critically analysed, and this leads to a new direction. To reconcile quantum with chaos and to restore genuine temporal chaos in quantum systems, a time-discrete variant of quantum dynamics is proposed.
Audience:This book will be of interest to graduate students and researchers in physics, chemistry and mathematics, whose work involves fundamental questions of quantum mechanics in chaotic systems.

• chaos
• chemistry
• mechanics
• nano-scale
• quantization
• quantum chaos
• quantum dynamics
• quantum mechanics
• scattering
• statistical mechanics

• Faculty of Engineering, Osaka City University, Osaka, Japan

  Katsuhiro Nakamura

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