000			04964nam a22005175i 4500
001			978-3-0348-0697-8
003			DE-He213
005			20140220082836.0
007			cr nn 008mamaa
008			131126s2013 sz | s |||| 0|eng d
020			_a9783034806978 _9978-3-0348-0697-8
024	7		_a10.1007/978-3-0348-0697-8 _2doi
050		4	_aQA313
072		7	_aPBWR _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.39 _223
082	0	4	_a515.48 _223
100	1		_aDuplantier, Bertrand. _eeditor.
245	1	0	_aChaos _h[electronic resource] : _bPoincaré Seminar 2010 / _cedited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau.
264		1	_aBasel : _bSpringer Basel : _bImprint: Birkhäuser, _c2013.
300			_aXII, 270 p. 100 illus., 61 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Mathematical Physics, _x1544-9998 ; _v66
505	0		_aForeword -- 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?.
520			_aThis 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.
650		0	_aMathematics.
650		0	_aDifferentiable dynamical systems.
650		0	_aNumber theory.
650	1	4	_aMathematics.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aNumber Theory.
650	2	4	_aQuantum Field Theories, String Theory.
650	2	4	_aStatistical Physics, Dynamical Systems and Complexity.
700	1		_aNonnenmacher, Stéphane. _eeditor.
700	1		_aRivasseau, Vincent. _eeditor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783034806961
830		0	_aProgress in Mathematical Physics, _x1544-9998 ; _v66
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-0348-0697-8
912			_aZDB-2-SMA
999			_c96330 _d96330