Albert C J Luo

Hamiltonian Chaos Beyond the KAM Theory: Dedicated to George M. Zaslavsky (1935-2008) - Nonlinear Physical Science Albert C J Luo

Marc Notes: Dedicated to Geroge M. Zaslavsky (1935-2008).; Includes bibliogdraphical references and index.; Also published by Higher Education Press, Beijing. Table of Contents: 1. Stochastic and Resonant Layers in Nonlinear Hamiltonian Systems / Albert C. J. Luo -- 1.1. Introduction -- 1.2. Stochastic layers -- 1.2.1. Geometrical description -- 1.2.2. Approximate criterions -- 1.3. Resonant layers -- 1.3.1. Layer dynamics -- 1.3.2. Approximate criterions -- 1.4. A periodically forced Duffing oscillator -- 1.4.1. Approximate predictions -- 1.4.2. Numerical illustrations -- 1.5. Discussions -- References -- 2. A New Approach to the Treatment of Separatrix Chaos and Its Applications / S. M. Soskin, R. Mannella, O. M. Yevtushenko, I. A. Khovanov, P. V. E. McClintock -- 2.1. Introduction -- 2.1.1. Heuristic results -- 2.1.2. Mathematical and accurate physical results -- 2.1.3. Numerical evidence for high peaks in ?E(?f) and their rough estimations -- 2.1.4. Accurate description of the peaks and of the related phenomena -- 2.2. Basic ideas of the approach -- 2.3. Single-separatrix chaotic layer -- 2.3.1. Rough estimates. Classification of systems -- 2.3.2. Asymptotic theory for systems of type I -- 2.3.3. Asymptotic theory for systems of type II -- 2.3.4. Estimate of the next-order corrections -- 2.3.5. Discussion -- 2.4. Double-separatrix chaos -- 2.4.1. Asymptotic theory for the minima of the spikes -- 2.4.2. Theory of the spikes' wings -- 2.4.3. Generalizations and applications -- 2.5. Enlargement of a low-dimensional stochastic web -- 2.5.1. Slow modulation of the wave angle -- 2.5.2. Application to semiconductor superlattices -- 2.5.3. Discussion -- 2.6. Conclusions -- 2.7. Appendix -- 2.7.1. Lower chaotic layer -- 2.7.2. Upper chaotic layer -- References -- 3. Hamiltonian Chaos and Anomalous Transport in Two Dimensional Flows / Xavier Leoncini -- 3.1. Introduction -- 3.2. Point vortices and passive tracers advection -- 3.2.1. Definitions -- 3.2.2. Chaotic advection -- 3.3. A system of point vortices -- 3.3.1. Definitions -- 3.4. Dynamics of systems with two or three point vortices -- 3.4.1. Dynamics of two vortices -- 3.4.2. Dynamics of three vortices -- 3.5. Vortex collapse and near collapse dynamics of point vortices -- 3.5.1. Vortex collapse -- 3.5.2. Vortex dynamics in the vicinity of the singularity -- 3.6. Chaotic advection and anomalous transport -- 3.6.1. A brief history -- 3.6.2. Definitions -- 3.6.3. Anomalous transport in incompressible flows -- 3.6.4. Tracers (passive particles) dynamics -- 3.6.5. Transport properties -- 3.6.6. Origin of anomalous transport -- 3.6.7. General remarks -- 3.7. Beyond characterizing transport -- 3.7.1. Chaos of field lines -- 3.7.2. Local Hamiltonian dynamics -- 3.7.3. An ABC type flow -- 3.8. Targeted mixing in an array of alternating vortices -- 3.9. Conclusion -- References -- 4. Hamiltonian Chaos with a Cold Atom in an Optical Lattice / S. V. Prants -- 4.1. Short historical background -- 4.2. Introduction -- 4.3. Semiclassical dynamics -- 4.3.1. Hamilton-Schrodinger equations of motion -- 4.3.2. Regimes of motion -- 4.3.3. Stochastic map for chaotic atomic transport -- 4.3.4. Statistical properties of chaotic transport -- 4.3.5. Dynamical fractals -- 4.4. Quantum dynamics -- 4.5. Dressed states picture and nonadiabatic transitions -- 4.5.1. Wave packet motion in the momentum space -- 4.6. Quantum-classical correspondence and manifestations of dynamical chaos in wave-packet atomic motion -- References -- 5. Using Stochastic Webs to Control the Quantum Transport of Electrons in Semiconductor Superlattices / T. M. Fromhold, A. A. Krokhin, S. Bujkiewicz, P. B. Wilkinson, D. Fowler, A. Patane, L. Eaves, D. P. A. Hardwick, A. G. Balanov, M. T. Greenaway, A. Henning -- 5.1. Introduction -- 5.2. Superlattice structures -- 5.3. Semiclassical electron dynamics -- 5.4. Electron drift velocity -- 5.5. Current-voltage characteristics: theory and experiment -- 5.6. Electrostatics and charge domain structure -- 5.7. Tailoring the SL structure to increase the number of conductance resonances -- 5.8. Energy eigenstates and Wigner functions -- 5.9. Summary and outlook -- References -- 6. Chaos in Ocean Acoustic Waveguide / A. L. Virovlyansky -- 6.1. Introduction -- 6.2. Basic equations -- 6.2.1. Parabolic equation approximation -- 6.2.2. Geometrical optics. Hamiltonian formalism -- 6.2.3. Modal representation of the wave field -- 6.2.4. Ray-based description of normal modes -- 6.3. Ray chaos -- 6.3.1. Statistical description of chaotic rays -- 6.3.2. Environmental model -- 6.3.3. Wiener process approximation -- 6.3.4. Distribution of ray parameters -- 6.3.5. Smoothed intensity of the wave field -- 6.4. Ray travel times -- 6.4.1. Timefront -- 6.4.2. Statistics of ray travel times -- 6.5. Modal structure of the wave field under conditions of ray chaos -- 6.5.1. Coarse-grained energy distribution between normal modes -- 6.5.2. Transient wave field -- 6.6. Conclusion -- References.