The Resource Chaos : Poincaré Seminar 2010, edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau, (electronic resource)

Chaos : Poincaré Seminar 2010, edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau, (electronic resource)

Label
Chaos : Poincaré Seminar 2010
Title
Chaos
Title remainder
Poincaré Seminar 2010
Statement of responsibility
edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau
Creator
Contributor
Editor
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Duplantier, Bertrand
Image bit depth
0
LC call number
QA313
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Nonnenmacher, Stéphane.
  • Rivasseau, Vincent.
  • SpringerLink
Series statement
Progress in Mathematical Physics,
Series volume
66
http://library.link/vocab/subjectName
  • Mathematics
  • Differentiable dynamical systems
  • Number theory
  • Mathematics
  • Dynamical Systems and Ergodic Theory
  • Number Theory
  • Quantum Field Theories, String Theory
  • Statistical Physics, Dynamical Systems and Complexity
Label
Chaos : Poincaré Seminar 2010, edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Foreword -- 1 Étienne Ghys, The Lorenz Attractor, a Paradigm for Chaos -- 2 Stéphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows -- 3 Uzy Smilansky, Discrete Graphs - A Paradigm Model for Quantum Chaos -- 4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann ζ-function -- 5 Hans-Jürgen Stöckmann, Chaos in Microwave Resonators -- 6 Stéphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates -- 7 Jacques Laskar, Is the Solar System Stable?
Dimensions
unknown
Extent
XII, 270 p. 100 illus., 61 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783034806978
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0697-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-0348-0697-8
Label
Chaos : Poincaré Seminar 2010, edited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Foreword -- 1 Étienne Ghys, The Lorenz Attractor, a Paradigm for Chaos -- 2 Stéphan Fauve, Chaotic Dynamos Generated by Fully Turbulent Flows -- 3 Uzy Smilansky, Discrete Graphs - A Paradigm Model for Quantum Chaos -- 4 Paul Bourgade and Jonathan P. Keating, Quantum Chaos, Random Matrix Theory, and the Riemann ζ-function -- 5 Hans-Jürgen Stöckmann, Chaos in Microwave Resonators -- 6 Stéphane Nonnenmacher, Anatomy of Quantum Chaotic Eigenstates -- 7 Jacques Laskar, Is the Solar System Stable?
Dimensions
unknown
Extent
XII, 270 p. 100 illus., 61 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783034806978
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-0348-0697-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-0348-0697-8

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