Progress in Mathematical Physics

Chaos

Poincaré Seminar 2010

Editors: Duplantier, Bertrand, Nonnenmacher, Stéphane, Rivasseau, Vincent (Eds.)

  • Renowned scientists present different facets of chaotic dynamics
  • Addresses students and researchers in physics and mathematics
  • Based on educational lectures given at the Institut Henri Poincaré in Paris
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About this book

This twelfth volume in the Poincaré Seminar Series presents a complete and interdisciplinary perspective on the concept of Chaos, both in classical mechanics in its deterministic version, and in quantum mechanics. This book expounds some of the most wide ranging questions in science, from uncovering the fingerprints of classical chaotic dynamics in quantum systems, to predicting the fate of our own planetary system. Its seven articles are also highly pedagogical, as befits their origin in lectures to a broad scientific audience. Highlights include a complete description by the mathematician É. Ghys of the paradigmatic Lorenz attractor, and of the famed Lorenz butterfly effect as it is understood today, illuminating the fundamental mathematical issues at play with deterministic chaos; a detailed account by the experimentalist S. Fauve of the masterpiece experiment, the von Kármán Sodium or VKS experiment, which established in 2007 the spontaneous generation of a magnetic field in a strongly turbulent flow, including its reversal, a model of Earth’s magnetic field; a simple toy model by the theorist U. Smilansky – the discrete Laplacian on finite d-regular expander graphs – which allows one to grasp the essential ingredients of quantum chaos, including its fundamental link to random matrix theory; a review by the mathematical physicists P. Bourgade and J.P. Keating, which illuminates the fascinating connection between the distribution of zeros of the Riemann ζ-function and the statistics of eigenvalues of random unitary matrices, which could ultimately provide a spectral interpretation for the zeros of the ζ-function, thus a proof of the celebrated Riemann Hypothesis itself; an article by a pioneer of experimental quantum chaos, H-J. Stöckmann, who shows in detail how experiments on the propagation of microwaves in 2D or 3D chaotic cavities beautifully verify theoretical predictions; a thorough presentation by the mathematical physicist S. Nonnenmacher of the “anatomy” of the eigenmodes of quantized chaotic systems, namely of their macroscopic localization properties, as ruled by the Quantum Ergodic theorem, and of the deep mathematical challenge posed by their fluctuations at the microscopic scale; a review, both historical and scientific, by the astronomer J. Laskar on the stability, hence the fate, of the chaotic Solar planetary system we live in, a subject where he made groundbreaking contributions, including the probabilistic estimate of possible planetary collisions. This book should be of broad general interest to both physicists and mathematicians.

Table of contents (7 chapters)

  • The Lorenz Attractor, a Paradigm for Chaos

    Ghys, Étienne

    Pages 1-54

  • Chaotic Dynamos Generated by Fully Turbulent Flows

    Fauve, Stéphan

    Pages 55-95

  • Discrete Graphs – A Paradigm Model for Quantum Chaos

    Smilansky, Uzy

    Pages 97-124

  • Quantum Chaos, Random Matrix Theory, and the Riemann ζ-function

    Bourgade, Paul (et al.)

    Pages 125-168

  • Chaos in Microwave Resonators

    Stöckmann, Hans-Jürgen

    Pages 169-191

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-0348-0697-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-0348-0696-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Chaos
Book Subtitle
Poincaré Seminar 2010
Editors
  • Bertrand Duplantier
  • Stéphane Nonnenmacher
  • Vincent Rivasseau
Series Title
Progress in Mathematical Physics
Series Volume
66
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0697-8
DOI
10.1007/978-3-0348-0697-8
Hardcover ISBN
978-3-0348-0696-1
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XII, 270
Number of Illustrations and Tables
39 b/w illustrations, 61 illustrations in colour
Topics