Chaotic Dynamics and Transport in Classical and Quantum Systems

This book offers a modern updated review on the most important activities in today dynamical systems and statistical mechanics by some of the best experts in the domain. It gives a contemporary and pedagogical view on theories of classical and quantum chaos and complexity in hamiltonian and ergodic systems and their applications to anomalous transport in fluids, plasmas, oceans and atom-optic devices and to control of chaotic transport. The book is issued from lecture notes of the International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems held in Cargèse (Corsica) 18th to the 30th August 2003. It reflects the spirit of the School to provide lectures at the post-doctoral level on basic concepts and tools. The first part concerns ergodicity and mixing, complexity and entropy functions, SRB measures, fractal dimensions and bifurcations in hamiltonian systems. Then, models of dynamical evolutions of transport processes in classical and quantum systems have been largely explained. The second part concerns transport in fluids, plasmas and reacting media. On the other hand, new experiments of cold optically trapped atoms and electrodynamics cavity have been thoroughly presented. Finally, several papers bears on synchronism and control of chaos.The target audience of the proceedings are physicists, mathematicians and all scientists involved in Chaos and Dynamical Systems Theory and their fundamental applications in Physics and in the Science of Complex and Nonlinear phenomena. TOC:From the contentsTheory: A Short Ergodic Theory Refresher. Notes on Spectral Theory, Mixing and Transport Complexity, Fractal Dimensions and Topological Entropy in Dynamical Systems. Working with Complexity Functions. SRB distribution for Anosov maps. Dynamical Systems Theory of Irreversibility. Aspects of Open Quantum System Dynamics. Energy Surfaces And Hierarchies of Bifurcations. Phase-Space Semiclassical Analysis. Around Semiclassical Trace Formulae.- Applications: Atom-Optics Billiards. Control of Chaos And Separation Of Particles in Inertia Ratchets. Fractal Time Random Walk And Subrecoil Laser Cooling Considered As Renewal Processes with Infinite Mean Waiting Times. Anomalous Transport in Two-Dimensional Plasma Turbulence. The Onset of Synchronism in Globally Coupled Ensembles of Chaotic And Periodic Dynamical Units. Quantum Breaking Time for Chaotic Systems With Phase Space Structures. Hamiltonian Chaos And Fractals in Cavity Quantum Electrodynamics. Inert And Reacting Transport. Anomalous Transport in Steady Plane Flows of Viscous Fluids. Tracer Transport during The Geostrophic Adjustment in The Equatorial Ocean. The Fermi-Pasta-Ulam Problem in The Thermodynamic Limit.