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This twelfth volume in the Poincare 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 E. 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 Karman 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
-function and the statistics of eigenvalues of random unitary
matrices, which could ultimately provide a spectral interpretation
for the zeros of the -function, thus a proof of the celebrated
Riemann Hypothesis itself; an article by a pioneer of experimental
quantum chaos, H-J. Stoeckmann, 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.
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