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Springer eBooks

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

Published Jan 1, 2002• 0 citations
Publisher
DOI
10.1007/0-306-47121-3_3

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•Jun 28, 2011•0 citations
Preface. 1. Genesis of Chaos and Breakdown of Quantization of Adiabatic Invariants. 2. Semiclassical Quantization of Chaos: Trace Formula. 3. Pseudo-Chaos Without Classical Counterpart in 1-Dimensional Quantum Transport. 4. Chaos and Quantum Transport in Open Magnetic Billiards: From Stadium to Sinai Billiards. 5. Chaotic Scattering on Hyperbolic Billiards: Success of Semiclassical Theory. 6. Nonadiabaticity-Induced Quantum Chaos. 7. Level Dynamics and Statistical Mechanics. 8. Towards Time-Discrete Quantum Mechanics. 9. Conclusions and Prospects. Index.
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.