Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos by N.E. HurtQuantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos by N.E. Hurt

Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of Chaos

byN.E. Hurt

Paperback | December 5, 2010

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This is the first monograph to present a comprehensive treatment of the mathematical foundations of quantum chaos. Precise results in this area involve an exciting mixture of analytical number theory, zeta and L-functions, random matrix theory, scattering theory, the Selberg trace formula, and related global functional analysis. Many examples are presented including polygonal and standard billiards systems and models on the pseudosphere. The physics of both compact and finite volume systems are discussed, as well as systems in the presence of a magnetic field. Results on the spectra of Gutzwiller models for mesoscopic systems are discussed including questions of dissolving eigenvalues, simplicity of the spectra and exceptional eigenvalues. Relationships to isometric-isospectral questions in physics are discussed. Finally, applications of quantum chaos to recent results on mesoscopic physics are discussed, in particular transport properties in these devices. Starting from simple examples, the text leads the reader through the most recent work of Sarnak, Luo and coworkers on arithmetic chaos, Zelditch, Degli Esposti and coworkers on quantum ergodicity, Bleher and coworkers on integrable systems, Gutkin, Veech and coworkers on polygonal billiards, Sarnak, Phillips and coworkers on spectra of Gutzwiller models, Mueller and others on scattering theory, Berry, Keating, Steiner, Aurich, Bolte, Schmit, Bogomolny and coworkers on quantum chaos and Marcus Beenakker and coworkers on mesoscopic systems. Audience: This book will be of use to physicists, mathematicians, and engineers interested in quantum chaos and its applications to mesoscopic systems.
Title:Quantum Chaos and Mesoscopic Systems: Mathematical Methods in the Quantum Signatures of ChaosFormat:PaperbackDimensions:350 pages, 9.61 × 6.69 × 0 inPublished:December 5, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048148111

ISBN - 13:9789048148110

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Table of Contents

Preface. 1. Signatures of Quantum Chaos. 2. Billiards: Polygonal and Others. 3. Quantum Transition Amplitudes. 4. Variance of Quantum Matrix Elements. 5. Error Terms. 6. Co-Finite Model for Quantum Chaology. 7. Landau Levels and L-Functions. 8. Wigner Time Delay. 9. Scattering Theory for Leaky Tori. 10. Dissolving Bound States. 11. Dissolving Eigenvalues. 12. Half-Integral Forms. 13. Isometric and Isospectral Manifolds. 14. Mesoscopic Structures. 15. References. Index.