Cargando…
Quantum chaos : Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991 /
The study of quantum systems which are chaotic in the classical limit (quantum chaos or quantum chaology) is a very new field of research. Not long ago, it was still considered as an esoteric subject, however this attitude changed radically when it was realized that this subject is relevant to many...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores Corporativos: | , |
| Otros Autores: | , , |
| Formato: | Electrónico Congresos, conferencias eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
North-Holland,
1993.
|
| Colección: | Proceedings of the International School of Physics "Enrico Fermi" ;
course 119 |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Quantum Chaos; Copyright Page; Table of Contents; Preface; Chapter 1. Hyperbolic Structure in Classical Chaos; 1. Introduction.; 2. Transverse homoclinic orbits; 3. Anti-integrable limit; 4. Interlude; 5. Anosov systems; 6. Nonzero Lyapunov exponents; 7. Flux; 8. Summary; A guide to the literature; APPENDIX: Mathematical notation; Chapter 2. A New Paradigm in Quantum Chaos: Aubry's Theory of Equilibrium States for the Adiabatic Holstein Model; 1. Introduction; 2. The model; 3. The anti-integrable limit t = 0; 4. Small hopping; 5. Explicit estimates; 6. Properties; 7. Extensions.
- APPENDIX A: Notation and basic mathematical resultsAPPENDIX B: Comments on the proof of [1]; APPENDIX C: Solution of a recurrence inequality; APPENDIX D: Variation of the electronic energy with configuration u; REFERENCES; Chapter 3. Periodic-Orbit Theory; 1. Introduction; 2. Semi-classical periodic-orbit theory; 3. Organizing chaos; 4. Symmetries; 5. The three-disk system; 6. Classical periodic-orbit theory; 7. Matrix elements; 8. Final remarks; REFERENCES; Chapter 4. The Semi-Classical Helium Atom.; 1. Introduction; 2. Classical motion in helium; 3. Semi-classical quantization.
- 4. Adiabatic vs. chaotic motion5. Summary and conclusions; REFERENCES; Chapter 5. The Riemann Zeta-Function and Quantum Chaology; 1. The Riemann zeta-function; 2. The functional equation; 3. The staircase of zeros; 4. The quantum chaology connection; 5. Convergence properties of periodic-orbit formulae; 6. Riemann-Siegel resummation; 7. The pair correlation of the zeros; APPENDIX: Probabilistic number theory and the pairwise distribution of the primes; REFERENCES; Chapter 6. Quantum Localization; 1. Introduction; 2. The kicked rotor; 3. Anderson localization.
- 4. The mapping of the kicked-rotor problem on the Anderson model5. Adiabatic localization; 6. Measures and manifestations of localization; 7. Summary; 8. Related problems; REFERENCES; Chapter 7. Dynamical Localization in the Hydrogen Atom; 1. Introduction; 2. Classical dynamics; 3. One-dimensional model; 4. Kepler map; 5. Photonic localization; 6. Derealization; 7. Quantization of the Kepler map and the scattering problem; 9. Conclusion; REFERENCES; Chapter 8. Dynamical Localization, Dissipation and Noise; 1. Introduction; 2. Dissipative quantum dynamics.
- 3. Dynamical localization in the dissipative kicked-rotor model4. Rydberg atoms in a noisy waveguide; REFERENCES; Chapter 9. Statistics of Quasi-Energy Spectrum.; 1. Introduction; 2. Some time-dependent models with classical chaos; 3. The kicked-rotator model; 4. General properties of the quasi-energy spectrum and quantum resonance; 5. Uncorrelated statistics of quasi-energy; 6. Maximal statistical properties of quasi-energy spectra; 7. Intermediate statistics caused by the localization; REFERENCES; Chapter 10. Scattering and Resonances: Classical and Quantum Dynamics.; 1. Introduction.