Casati / Guarneri / Smilansky Quantum Chaos

1. Auflage 2015
ISBN: 978-1-4832-9032-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 119, 437 Seiten, Web PDF

Reihe: Enrico Fermi International School of Physics

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 of the more mature branches of physics.This book presents the accumulated knowledge available up until now and at the same time introduces topics which are being intensively studied at present. Their relevance to other fields such as condensed matter, atomic and nuclear physics is also discussed. The lectures have been divided into two rough categories - background and advanced lectures.

Autoren/Hrsg.

Casati, G.

Guarneri, I.

Smilansky, U.

Inhaltsverzeichnis

1;Front Cover;1
2;Quantum Chaos;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;12
6;Chapter 1. Hyperbolic Structure in Classical Chaos;20
6.1;1. Introduction.;20
6.2;2. Transverse homoclinic orbits;27
6.3;3. Anti-integrable limit;37
6.4;4. Interlude;41
6.5;5. Anosov systems;43
6.6;6. Nonzero Lyapunov exponents;52
6.7;7. Flux;55
6.8;8. Summary;65
6.9;A guide to the literature;65
6.10;APPENDIX: Mathematical notation;66
7;Chapter 2. A New Paradigm in Quantum Chaos: Aubry's Theory of Equilibrium States for the Adiabatic Holstein Model;70
7.1;1. Introduction;70
7.2;2. The model;70
7.3;3. The anti-integrable limit t = 0;71
7.4;4. Small hopping;72
7.5;5. Explicit estimates;75
7.6;6. Properties;82
7.7;7. Extensions;86
7.8;APPENDIX A: Notation and basic mathematical results;88
7.9;APPENDIX B: Comments on the proof of [1];89
7.10;APPENDIX C: Solution of a recurrence inequality;91
7.11;APPENDIX D: Variation of the electronic energy with configuration u;92
7.12;REFERENCES;94
8;Chapter 3. Periodic-Orbit Theory;96
8.1;1. Introduction;96
8.2;2. Semi-classical periodic-orbit theory;98
8.3;3. Organizing chaos;103
8.4;4. Symmetries;111
8.5;5. The three-disk system;116
8.6;6. Classical periodic-orbit theory;122
8.7;7. Matrix elements;125
8.8;8. Final remarks;127
8.9;REFERENCES;128
9;Chapter 4. The Semi-Classical Helium Atom.;132
9.1;1. Introduction;132
9.2;2. Classical motion in helium;134
9.3;3. Semi-classical quantization;143
9.4;4. Adiabatic vs. chaotic motion;157
9.5;5. Summary and conclusions;160
9.6;REFERENCES;161
10;Chapter 5. The Riemann Zeta-Function and Quantum Chaology;164
10.1;1. The Riemann zeta-function;166
10.2;2. The functional equation;168
10.3;3. The staircase of zeros;170
10.4;4. The quantum chaology connection;172
10.5;5. Convergence properties of periodic-orbit formulae;177
10.6;6. Riemann-Siegel resummation;183
10.7;7. The pair correlation of the zeros;192
10.8;APPENDIX: Probabilistic number theory and the pairwise distribution of the primes;200
10.9;REFERENCES;203
11;Chapter 6. Quantum Localization;206
11.1;1. Introduction;206
11.2;2. The kicked rotor;207
11.3;3. Anderson localization;211
11.4;4. The mapping of the kicked-rotor problem on the Anderson model;216
11.5;5. Adiabatic localization;222
11.6;6. Measures and manifestations of localization;226
11.7;7. Summary;233
11.8;8. Related problems;233
11.9;REFERENCES;234
12;Chapter 7. Dynamical Localization in the Hydrogen Atom;240
12.1;1. Introduction;240
12.2;2. Classical dynamics;242
12.3;3. One-dimensional model;244
12.4;4. Kepler map;245
12.5;5. Photonic localization;248
12.6;6. Derealization;251
12.7;7. Quantization of the Kepler map and the scattering problem;254
12.8;9. Conclusion;255
12.9;REFERENCES;256
13;Chapter 8. Dynamical Localization, Dissipation and Noise;260
13.1;1. Introduction;260
13.2;2. Dissipative quantum dynamics;263
13.3;3. Dynamical localization in the dissipative kicked-rotor model;269
13.4;4. Rydberg atoms in a noisy waveguide;277
13.5;REFERENCES;283
14;Chapter 9. Statistics of Quasi-Energy Spectrum.;284
14.1;1. Introduction;284
14.2;2. Some time-dependent models with classical chaos;287
14.3;3. The kicked-rotator model;290
14.4;4. General properties of the quasi-energy spectrum and quantum resonance;295
14.5;5. Uncorrelated statistics of quasi-energy;300
14.6;6. Maximal statistical properties of quasi-energy spectra;303
14.7;7. Intermediate statistics caused by the localization;309
14.8;REFERENCES;323
15;Chapter 10. Scattering and Resonances: Classical and Quantum Dynamics.;326
15.1;1. Introduction;326
15.2;2. Classical scattering and chaotic repellers;327
15.3;3. Semi-classical quantum scattering;364
15.4;4. Conclusions;393
15.5;REFERENCES;399
16;Chapter 11. Exotic Fractals and Atomic Decay.;404
16.1;1. Introduction;404
16.2;2. What is the one-dimensional kicked hydrogen atom (1DKH)?;405
16.3;3. Why consider the 1DKH?;405
16.4;4. Equations of motion;406
16.5;5. The mapping;408
16.6;6. The never-come-back property;409
16.7;7. The Jacobian;410
16.8;8. Eigenvalues;410
16.9;9. Hyperbolicity;411
16.10;10. The tent map, a model for ionization;414
16.11;11. Power law decay of the 1DKH;415
16.12;12. Exotic (scale-broken) fractals;415
16.13;13. Summary;416
16.14;REFERENCES;416
17;Chapter 12. Quantum Chaotic Scattering and Microwave Experiments.;418
17.1;1. Introduction;418
17.2;2. The model;420
17.3;3. Semi-classical theory;423
17.4;4. S-matrix element energy correlations;423
17.5;5. S-matrix correlations under general perturbations;424
17.6;6. The Wigner time delay;427
17.7;7. Absorption;428
17.8;8. Conclusions;431
17.9;REFERENCES;431