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Chaotic Dynamics and Transport in Classical and Quantum Systems

Proceedings of the NATO Advanced Study Institute on International Summer School on Chaotic Dynamics and Transport in Classical and Quantum Systems, Cargèse, Corsica, 18 - 30 August 2003.

  • Conference proceedings
  • © 2005

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Editors:
  1. P. Collet

    1. Ecole Polytechnique, Paris, France

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  2. M. Courbage

    1. Université Paris 7-Denis Diderot, France

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  3. S. Métens

    1. Université Paris 7-Denis Diderot, France

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  4. A. Neishtadt

    1. Space Research Institute, Moscow, Russia

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  5. G. Zaslavsky

    1. New-York University, New York, USA

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Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 182)

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About this book

From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).

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Table of contents (20 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Theory

    1. A Short Ergodic Theory Refresher

      • P. Collet
      Pages 1-14

    2. Notes on Spectral Theory, Mixing and Transport

      • Maurice Courbage
      Pages 15-33

    3. Complexity, Fractal Dimensions and Topological Entropy in Dynamical Systems

      • Valentin Affraimovich, Lev Glebsky
      Pages 35-72

    4. Working with Complexity Functions

      • G. M. Zaslavsky, V. Afraimovich
      Pages 73-85

    5. SRB distribution for Anosov maps

      • Giovanni Gallavotti
      Pages 87-105

    6. Dynamical Systems Theory of Irreversibility

      • Pierre Gaspard
      Pages 107-157

    7. Aspects of Open Quantum System Dynamics

      • Walter T. Strunz
      Pages 159-187

    8. Energy Surfaces and Hierarchies of Bifurcations

      • Eli Shlizerman, Vered Rom-Kedar
      Pages 189-223

    9. Phase-Space Semiclassical Analysis. Around Semiclassical Trace Formulae

      • Monique Combescure
      Pages 225-238

  3. Applications

    1. Atom-Optics Billiards

      • Ariel Kaplan, Mikkel Andersen, Nir Friedman, Nir Davidson
      Pages 239-267

    2. Control of Chaos and Separation of Particles in Inertia Ratchets

      • Fereydoon Family, C. Miguel Arizmendi, Hilda A. Larrondo
      Pages 269-280

    3. Fractal Time Random Walk and Subrecoil Laser Cooling Considered as Renewal Processes with Infinite Mean Waiting Times

      • F. Bardou
      Pages 281-301

    4. Anomalous Transport in Two-Dimensional Plasma Turbulence

      • Xavier Leoncini, Olivier Agullo, Sadruddin Benkadda, George M. Zaslavsky
      Pages 303-319

    5. The Onset of Synchronism in Globally Coupled Ensembles of Chaotic and Periodic Dynamical Units

      • Edward Ott, Paul So, Ernest Barreto, Thomas Antonsen
      Pages 321-331

    6. Quantum Breaking Time for Chaotic Systems with Phase Space Structures

      • A. Iomin, G.M. Zaslavsky
      Pages 333-348

    7. Hamiltonian Chaos and Fractals in Cavity Quantum Electrodynamics

      • S.V. Prants
      Pages 349-363

    8. Inert and Reacting Transport

      • M. Cencini, D. Vergni, A. Vulpiani
      Pages 365-399

    9. Anomalous Transport in Steady Plane Flows of Viscous Fluids

      • Michael A. Zaks
      Pages 401-412

    10. Tracer Transport During the Geostrophic Adjustment in the Equatorial Ocean

      • J. Le Sommer, V. Zeitlin
      Pages 413-429
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Editors and Affiliations

  • Ecole Polytechnique, Paris, France

    P. Collet

  • Université Paris 7-Denis Diderot, France

    M. Courbage, S. Métens

  • Space Research Institute, Moscow, Russia

    A. Neishtadt

  • New-York University, New York, USA

    G. Zaslavsky

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