Quantum Chaos Y2k : Proceedings of Nobel Symposium 116, Backaskog Castle, Sweden, June 13-17 2000.

By: Berggren, Karl-FredrikContributor(s): Aberg, Sven | Staff, Physica ScriptaSeries: Proceedings of Nobel Symposium - Physics SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2001Copyright date: ©2001Description: 1 online resource (286 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789812811004Subject(s): Quantum chaos -- Congresses.;Quantum theory -- CongressesGenre/Form: Electronic books. Additional physical formats: Print version:: Quantum Chaos Y2k : Proceedings of Nobel Symposium 116, Backaskog Castle, Sweden, June 13-17 2000DDC classification: 530.12 LOC classification: QC174.17.C45N63 2000Online resources: Click to View
Contents:
Intro -- Contents -- Committees -- List of participants -- Introduction -- Quantum Chaos Y2K After-dinner speech by Martin C. Gutzwiller -- Spectral twinkling: A new example of singularity-dominated strong fluctuations (summary) -- Quantum chaos in GaAs/AlxGa1-xAs microstructures -- 1. Introduction -- 2. Weak-location In chaotic versus non-chaotic cavities: a striking difference in the line shape -- 3. Non-gaussian distribution of coulomb blockade peak heights in quantum dots -- 4. Pairing effect in ultra-small quantum dots -- Ground state spin and Coulomb blockade peak motion in chaotic quantum dots -- 1. Introduction -- 2. Theory -- 3. Experiment -- 4. Discussion -- Quantum chaos and transport phenomena in quantum dots -- Conductance of a ballistic electron billiard in a magnetic field: Does the semiclassical approach apply? -- 1. Introduction -- 2. Semi-classical conductance calculations -- 3. Discussion and Conclusions -- Semiconductor billiards - a controlled environment to study fractals -- 1. Introduction -- 2. Background: the semiconductor Sinai billiard -- 3. Fractal conductance fluctuations - observation of exact self-affinity -- 4. Fractal conductance fluctuations - observation of statistical self-affinity -- 5. Discussion -- 6. Conclusions -- Experimental signatures of wavefunction scarring in open semiconductor billiards -- Chaos in quantum ratchets -- 1. Introduction -- 2. Quantum ratchets -- 3. Chaotic behaviour of classical ratchets -- 4. Quantum chaos in rocking ratchets? -- 5. Experiment -- 6. Conclusion -- Statistics of resonances in open billiards -- The exterior and interior edge states of magnetic billiards: Spectral statistics and correlations -- 1. Introduction -- 2. The quantized magnetic billiard -- 3. The spectral density edge of states -- 4. Spectral analysis -- 5. Conclusions.
Non-universality of chaotic classical dynamics: implications for quantum chaos -- 1. Introduction -- 2. Non-universality of long-time dynamics -- 3. Fluctuations of periodic orbit density -- 4. Bifurcations as a mechanism for periodic orbit correlation -- 5. Conclusions concerning action correlations -- Chaos and interactions in quantum dots -- 1. Quantum dots -- 2. Transport in the Coulomb blockade regime -- 3. Signatures of chaos in closed dots -- 4. Interaction effects -- 5. Conclusions -- Stochastic aspects of many-body systems: The embedded Gaussian ensembles -- 1. Introduction -- 2. Definitions -- 3. Invariant decomposition of A(k) -- 4. Supersymmetry -- 5. Stability of the Saddle Point -- 6. Summary and Conclusions -- Quantum-classical correspondence for isolated systems of interacting particles: Localization and ergodicity in energy space -- 1. Introduction -- 2. Random matrix models -- 3. LDOS : Breit-Wigner region -- 4. LDOS : Transition to the Gaussian -- 5. Distribution of occupation numbers -- 6. Quantum-classical correspondence -- 7. Two interacting spins -- 8. One particle in a rippled channel -- 9. Localization and non-ergodicity in the energy shell -- Effect of symmetry breaking on statistical distributions -- 1. Introduction -- 2. General Background -- 3. Experimental Methods -- 4. Experimental Results - Level Statistics -- 5. Experimental Results - Transitions -- 6. Analysis -- 7. Summary -- 8. Acknowledgments -- Quantum chaos and quantum computers -- 1. Introduction -- 2. Aberg criterion for emergence of quantum chaos in many-body systems -- 3. Standard generic quantum computer model -- 4. Time scales for quantum chaos and decoherence in quantum computing -- 5. Conclusion -- Disorder and quantum chromodynamics - non-linear o models -- 1. Introduction -- 2. Gauge fields disorder and Thouless energy -- 3. Two non-linear o models.
4. Conclusions -- Correlations between periodic orbits and their role in spectral statistics -- 1. Introduction -- 2. Off-diagonal contributions to the form factor -- 3. Discussion and Conclusions -- 4. Appendix: The density of angles of self-intersection -- Quantum spectra and wave functions in terms of periodic orbits for weakly chaotic systems -- 1. Special quantum states -- 2. Some examples -- 3. Finding and approximating special states -- 4. More examples -- 5. Summary -- Bifurcation of periodic orbit as semiclassical origin of superdeformed shell structure -- 1. Introduction -- 2. Nuclear superdeformation -- 3. Spheroidal cavity model -- 4. Bifurcation of periodic orbit -- 5. Constant-action lines and Fourier transform -- 6. Semiclassical method capable of treating the bifurcation -- 7. Concluding remarks -- Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics -- Neutron stars and quantum billiards -- Scars and other weak localization effects in classically chaotic systems -- 1. Introduction -- 2. Measures of ergodicity -- 3. Examples of localization -- 4. Sinai billiard -- 5. Conclusion -- Tunneling and chaos -- 1. Introduction -- 2. Preliminaries -- 3. Near-integrable systems -- 4. Mixed phase space systems -- 5. Fully chaotic systems -- 6. Summary -- Relaxation and fluctuations in quantum chaos -- 1. Introduction -- 2. Quantum Poincare recurrences -- 3. Ionization rate in Rydberg atoms -- 4. Quantum fractal fluctuations -- Rydberg electrons in crossed fields: A paradigm for nonlinear dynamics beyond two degrees of freedom -- 1. Introduction -- 2. A new diagnostic tool: frequency map analysis -- 3. The Rydberg atom in static crossed fields -- 4. Microwave ionization in more than two degrees of freedom -- 5. Chaotic scattering in the crossed-fields problem.
Classical analysis of correlated multiple ionization in strong fields -- 1. Introduction -- 2. The model -- 3. Symmetric double ionization -- 4. The saddle and three-dimensional motions -- 5. Triple and higher ionization -- 6. Final remarks -- Classically-forbidden processes in photoabsorption spectra -- 1. Introduction -- 2. Classically-forbidden above-barrier-reflection -- 3. Absorption into a classically-forbidden region -- Quantum Hall Effect Breakdown Steps due to an instability of Laminar Flow against Electron-Hole Pair Formation -- 1. Overview -- 2. Quantum hall effect breakdown -- 3. A model for the steps: QHE breakdown due to inter-Landau level tunnelling -- 4. Analogies with classical hydrodynamics and quantum fluids -- Dynamical and wave chaos in the Bose-Einstein condensate -- 1. Introduction to Bose-Einstein condensation -- 2. The non-linear Schrodinger equation -- 3. Chaotic collapse of a growing attractive condensate -- 4. Phase imprinting as a control of condensate dynamics -- 5. Dynamical chaos in the BEC: soliton instabilities -- 6. Symmetry breaking and phase rigidity -- 7. Wave chaos: production of Bose-Einstein Speckle (BES) -- 8. Statistical properties of BES: first investigations -- 9. Summary and conclusions -- Wave Dynamical Chaos: An Experimental Approach in Billiards -- 1. Introduction -- 2. Experimental methods -- 3. First example: test of trace formulas for spectra in billiards of varying chaoticity -- 4. Second example: wave functions in a parametric billiard and the topological structure of exceptional points -- 5. Conclusion -- Acoustic chaos -- 1. Introduction -- 2. Acoustics -- 3. Symmetries -- 4. Wavefunctions -- 5. Width distributions -- 6. Conclusions -- Ultrasound resonances in a rectangular plate described by random matrices -- 1. Introduction -- 2. Experimental setup -- 3. Dispersion relations and Weyl law.
4. Ultrasound transmission spectrum -- 5. Mode separation -- 6. Spectral fluctuation statistics -- 7. Mode mixing and special states -- 8. Standing wave patterns -- 9. Conclusion -- Quantum correlations and classical resonances in an open chaotic system -- 1. Introduction -- 2. Experimental results -- 3. Quantum and classical correlations -- 4. Discussion and concluding remarks -- Why do an experiment if theory is exact and any experiment can at best approximate theory? -- Wave-Chaotic optical resonators and lasers -- 1. Introduction -- 2. Optical resonators and ARCs -- 3. ARCs as open quantum billiards -- 4. Refractive escape -- 5. Summary of the ray model -- 6. Resonance widths for chaotic WG modes -- 7. Quantum/wave corrections to the ray model -- 8. Directional emission from ARCs -- 9. Experimental evidence for chaotic whispering gallery modes -- 10. High Index ARCs and semiconductor microlasers -- 11. Mode selection and the power puzzle -- 12. Scarred lasing modes -- 13. Semiclassical theory for ARCs -- 14. Summary and conclusions -- Angular momentum localization in oval billiards -- Chaos and time-reversed acoustics -- 1. Introduction -- 2. Time reversal cavities and mirrors -- 3. Times reversal experiments -- 4. Conclusion -- Single-mode delay time statistics for scattering by a chaotic cavity -- 1. Introduction -- 2. Formulation of the problem -- 3. Small number of modes -- 4. Large number of modes -- 5. Numerical check -- 6. Conclusion.
Summary: Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium. Contents: After-Dinner Speech (M C Gutzwiller); Spectral Twinkling: A New Example of Singularity-Dominated Strong Fluctuations (Summary) (M Berry); Ground State Spin and Coulomb Blockade Peak Motion in Chaotic Quantum Dots (J A Folk et al.); Quantum Chaos and Transport Phenomena in Quantum Dots (A S Sachrajda); Chaos in Quantum Ratchets (H Linke et al.); Non-Universality of Chaotic Classical Dynamics: Implications for Quantum Chaos (M Wilkinson); Chaos and Interactions in Quantum Dots (Y Alhassid); Stochastic Aspects of Many-Body Systems: The Embedded Gaussian Ensembles (H A Weidenmüller); Effect of Symmetry Breaking on Statistical Distributions (G E Mitchell & J F Shriner, Jr.); Quantum Chaos and Quantum Computers (D L Shepelyansky); Disorder and Quantum Chromodynamics - Non-Linear σ Models (T Guhr & T Wilke); Correlation BetweenSummary: Periodic Orbits and Their Rôle in Spectral Statistics (M Sieber & K Richter); Neutron Stars and Quantum Billiards (A Bulgac & P Magierski); Tunneling and Chaos (S Tomsovic); Relaxation and Fluctuations in Quantum Chaos (G Casati); Scars and Other Weak Localization Effects in Classically Chaotic Systems (E J Heller); Classically-Forbidden Processes in Photoabsorption Spectra (J B Delos et al.); Wave Dynamical Chaos: An Experimental Approach in Billiards (A Richter); Acoustic Chaos (C Ellegaard et al.); Wave-Chaotic Optical Resonators and Lasers (A D Stone); Angular Momentum Localization in Oval Billiards (J U Nöckel); Chaos and Time-Reversed Acoustics (M Fink); and other papers. Readership: Quantum, nuclear, atomic, condensed matter and high energy physicists, as well as researchers in classical wave physics.
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Intro -- Contents -- Committees -- List of participants -- Introduction -- Quantum Chaos Y2K After-dinner speech by Martin C. Gutzwiller -- Spectral twinkling: A new example of singularity-dominated strong fluctuations (summary) -- Quantum chaos in GaAs/AlxGa1-xAs microstructures -- 1. Introduction -- 2. Weak-location In chaotic versus non-chaotic cavities: a striking difference in the line shape -- 3. Non-gaussian distribution of coulomb blockade peak heights in quantum dots -- 4. Pairing effect in ultra-small quantum dots -- Ground state spin and Coulomb blockade peak motion in chaotic quantum dots -- 1. Introduction -- 2. Theory -- 3. Experiment -- 4. Discussion -- Quantum chaos and transport phenomena in quantum dots -- Conductance of a ballistic electron billiard in a magnetic field: Does the semiclassical approach apply? -- 1. Introduction -- 2. Semi-classical conductance calculations -- 3. Discussion and Conclusions -- Semiconductor billiards - a controlled environment to study fractals -- 1. Introduction -- 2. Background: the semiconductor Sinai billiard -- 3. Fractal conductance fluctuations - observation of exact self-affinity -- 4. Fractal conductance fluctuations - observation of statistical self-affinity -- 5. Discussion -- 6. Conclusions -- Experimental signatures of wavefunction scarring in open semiconductor billiards -- Chaos in quantum ratchets -- 1. Introduction -- 2. Quantum ratchets -- 3. Chaotic behaviour of classical ratchets -- 4. Quantum chaos in rocking ratchets? -- 5. Experiment -- 6. Conclusion -- Statistics of resonances in open billiards -- The exterior and interior edge states of magnetic billiards: Spectral statistics and correlations -- 1. Introduction -- 2. The quantized magnetic billiard -- 3. The spectral density edge of states -- 4. Spectral analysis -- 5. Conclusions.

Non-universality of chaotic classical dynamics: implications for quantum chaos -- 1. Introduction -- 2. Non-universality of long-time dynamics -- 3. Fluctuations of periodic orbit density -- 4. Bifurcations as a mechanism for periodic orbit correlation -- 5. Conclusions concerning action correlations -- Chaos and interactions in quantum dots -- 1. Quantum dots -- 2. Transport in the Coulomb blockade regime -- 3. Signatures of chaos in closed dots -- 4. Interaction effects -- 5. Conclusions -- Stochastic aspects of many-body systems: The embedded Gaussian ensembles -- 1. Introduction -- 2. Definitions -- 3. Invariant decomposition of A(k) -- 4. Supersymmetry -- 5. Stability of the Saddle Point -- 6. Summary and Conclusions -- Quantum-classical correspondence for isolated systems of interacting particles: Localization and ergodicity in energy space -- 1. Introduction -- 2. Random matrix models -- 3. LDOS : Breit-Wigner region -- 4. LDOS : Transition to the Gaussian -- 5. Distribution of occupation numbers -- 6. Quantum-classical correspondence -- 7. Two interacting spins -- 8. One particle in a rippled channel -- 9. Localization and non-ergodicity in the energy shell -- Effect of symmetry breaking on statistical distributions -- 1. Introduction -- 2. General Background -- 3. Experimental Methods -- 4. Experimental Results - Level Statistics -- 5. Experimental Results - Transitions -- 6. Analysis -- 7. Summary -- 8. Acknowledgments -- Quantum chaos and quantum computers -- 1. Introduction -- 2. Aberg criterion for emergence of quantum chaos in many-body systems -- 3. Standard generic quantum computer model -- 4. Time scales for quantum chaos and decoherence in quantum computing -- 5. Conclusion -- Disorder and quantum chromodynamics - non-linear o models -- 1. Introduction -- 2. Gauge fields disorder and Thouless energy -- 3. Two non-linear o models.

4. Conclusions -- Correlations between periodic orbits and their role in spectral statistics -- 1. Introduction -- 2. Off-diagonal contributions to the form factor -- 3. Discussion and Conclusions -- 4. Appendix: The density of angles of self-intersection -- Quantum spectra and wave functions in terms of periodic orbits for weakly chaotic systems -- 1. Special quantum states -- 2. Some examples -- 3. Finding and approximating special states -- 4. More examples -- 5. Summary -- Bifurcation of periodic orbit as semiclassical origin of superdeformed shell structure -- 1. Introduction -- 2. Nuclear superdeformation -- 3. Spheroidal cavity model -- 4. Bifurcation of periodic orbit -- 5. Constant-action lines and Fourier transform -- 6. Semiclassical method capable of treating the bifurcation -- 7. Concluding remarks -- Wavefunction localization and its semiclassical description in a 3-dimensional system with mixed classical dynamics -- Neutron stars and quantum billiards -- Scars and other weak localization effects in classically chaotic systems -- 1. Introduction -- 2. Measures of ergodicity -- 3. Examples of localization -- 4. Sinai billiard -- 5. Conclusion -- Tunneling and chaos -- 1. Introduction -- 2. Preliminaries -- 3. Near-integrable systems -- 4. Mixed phase space systems -- 5. Fully chaotic systems -- 6. Summary -- Relaxation and fluctuations in quantum chaos -- 1. Introduction -- 2. Quantum Poincare recurrences -- 3. Ionization rate in Rydberg atoms -- 4. Quantum fractal fluctuations -- Rydberg electrons in crossed fields: A paradigm for nonlinear dynamics beyond two degrees of freedom -- 1. Introduction -- 2. A new diagnostic tool: frequency map analysis -- 3. The Rydberg atom in static crossed fields -- 4. Microwave ionization in more than two degrees of freedom -- 5. Chaotic scattering in the crossed-fields problem.

Classical analysis of correlated multiple ionization in strong fields -- 1. Introduction -- 2. The model -- 3. Symmetric double ionization -- 4. The saddle and three-dimensional motions -- 5. Triple and higher ionization -- 6. Final remarks -- Classically-forbidden processes in photoabsorption spectra -- 1. Introduction -- 2. Classically-forbidden above-barrier-reflection -- 3. Absorption into a classically-forbidden region -- Quantum Hall Effect Breakdown Steps due to an instability of Laminar Flow against Electron-Hole Pair Formation -- 1. Overview -- 2. Quantum hall effect breakdown -- 3. A model for the steps: QHE breakdown due to inter-Landau level tunnelling -- 4. Analogies with classical hydrodynamics and quantum fluids -- Dynamical and wave chaos in the Bose-Einstein condensate -- 1. Introduction to Bose-Einstein condensation -- 2. The non-linear Schrodinger equation -- 3. Chaotic collapse of a growing attractive condensate -- 4. Phase imprinting as a control of condensate dynamics -- 5. Dynamical chaos in the BEC: soliton instabilities -- 6. Symmetry breaking and phase rigidity -- 7. Wave chaos: production of Bose-Einstein Speckle (BES) -- 8. Statistical properties of BES: first investigations -- 9. Summary and conclusions -- Wave Dynamical Chaos: An Experimental Approach in Billiards -- 1. Introduction -- 2. Experimental methods -- 3. First example: test of trace formulas for spectra in billiards of varying chaoticity -- 4. Second example: wave functions in a parametric billiard and the topological structure of exceptional points -- 5. Conclusion -- Acoustic chaos -- 1. Introduction -- 2. Acoustics -- 3. Symmetries -- 4. Wavefunctions -- 5. Width distributions -- 6. Conclusions -- Ultrasound resonances in a rectangular plate described by random matrices -- 1. Introduction -- 2. Experimental setup -- 3. Dispersion relations and Weyl law.

4. Ultrasound transmission spectrum -- 5. Mode separation -- 6. Spectral fluctuation statistics -- 7. Mode mixing and special states -- 8. Standing wave patterns -- 9. Conclusion -- Quantum correlations and classical resonances in an open chaotic system -- 1. Introduction -- 2. Experimental results -- 3. Quantum and classical correlations -- 4. Discussion and concluding remarks -- Why do an experiment if theory is exact and any experiment can at best approximate theory? -- Wave-Chaotic optical resonators and lasers -- 1. Introduction -- 2. Optical resonators and ARCs -- 3. ARCs as open quantum billiards -- 4. Refractive escape -- 5. Summary of the ray model -- 6. Resonance widths for chaotic WG modes -- 7. Quantum/wave corrections to the ray model -- 8. Directional emission from ARCs -- 9. Experimental evidence for chaotic whispering gallery modes -- 10. High Index ARCs and semiconductor microlasers -- 11. Mode selection and the power puzzle -- 12. Scarred lasing modes -- 13. Semiclassical theory for ARCs -- 14. Summary and conclusions -- Angular momentum localization in oval billiards -- Chaos and time-reversed acoustics -- 1. Introduction -- 2. Time reversal cavities and mirrors -- 3. Times reversal experiments -- 4. Conclusion -- Single-mode delay time statistics for scattering by a chaotic cavity -- 1. Introduction -- 2. Formulation of the problem -- 3. Small number of modes -- 4. Large number of modes -- 5. Numerical check -- 6. Conclusion.

Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium. Contents: After-Dinner Speech (M C Gutzwiller); Spectral Twinkling: A New Example of Singularity-Dominated Strong Fluctuations (Summary) (M Berry); Ground State Spin and Coulomb Blockade Peak Motion in Chaotic Quantum Dots (J A Folk et al.); Quantum Chaos and Transport Phenomena in Quantum Dots (A S Sachrajda); Chaos in Quantum Ratchets (H Linke et al.); Non-Universality of Chaotic Classical Dynamics: Implications for Quantum Chaos (M Wilkinson); Chaos and Interactions in Quantum Dots (Y Alhassid); Stochastic Aspects of Many-Body Systems: The Embedded Gaussian Ensembles (H A Weidenmüller); Effect of Symmetry Breaking on Statistical Distributions (G E Mitchell & J F Shriner, Jr.); Quantum Chaos and Quantum Computers (D L Shepelyansky); Disorder and Quantum Chromodynamics - Non-Linear σ Models (T Guhr & T Wilke); Correlation Between

Periodic Orbits and Their Rôle in Spectral Statistics (M Sieber & K Richter); Neutron Stars and Quantum Billiards (A Bulgac & P Magierski); Tunneling and Chaos (S Tomsovic); Relaxation and Fluctuations in Quantum Chaos (G Casati); Scars and Other Weak Localization Effects in Classically Chaotic Systems (E J Heller); Classically-Forbidden Processes in Photoabsorption Spectra (J B Delos et al.); Wave Dynamical Chaos: An Experimental Approach in Billiards (A Richter); Acoustic Chaos (C Ellegaard et al.); Wave-Chaotic Optical Resonators and Lasers (A D Stone); Angular Momentum Localization in Oval Billiards (J U Nöckel); Chaos and Time-Reversed Acoustics (M Fink); and other papers. Readership: Quantum, nuclear, atomic, condensed matter and high energy physicists, as well as researchers in classical wave physics.

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