Quantum chaos : Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991 /: Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991. (1993)
- Record Type:
- Book
- Title:
- Quantum chaos : Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991 /: Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991. (1993)
- Main Title:
- Quantum chaos : Varenna on Lake Como, Villa Monsatero, 23 July -2 August, 1991
- Further Information:
- Note: Edited by G. Casati, I. Guarneri, and U. Smilansky.
- Editors:
- Casati, Giulio, 1942-
Guarneri, I
Smilansky, U - Other Names:
- Società italiana di fisica.
International School of Physics "Enrico Fermi" - Contents:
- 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.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 … (more)
- Publisher Details:
- Amsterdam : North-Holland
- Publication Date:
- 1993
- Extent:
- 1 online resource (xiii, 413 pages), illustrations
- Subjects:
- 530.1/2
Quantum chaos -- Congresses
Chaos quantique -- Congrès
Quantum chaos
SCIENCE / Energy
SCIENCE / Mechanics / General
SCIENCE / Physics / General
Igneous rocks
Conference papers and proceedings
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9781483290324
1483290328 - Related ISBNs:
- 9780444815880
- Notes:
- Note: Includes bibliographical references.
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