LEADER 06146nam 22008055 450 001 9910437864003321 005 20200701093521.0 010 $a3-0348-0697-3 024 7 $a10.1007/978-3-0348-0697-8 035 $a(CKB)3710000000031214 035 $a(EBL)1592530 035 $a(SSID)ssj0001067255 035 $a(PQKBManifestationID)11612779 035 $a(PQKBTitleCode)TC0001067255 035 $a(PQKBWorkID)11079447 035 $a(PQKB)10683487 035 $a(DE-He213)978-3-0348-0697-8 035 $a(MiAaPQ)EBC1592530 035 $a(PPN)176102965 035 $a(EXLCZ)993710000000031214 100 $a20131126d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aChaos $ePoincaré Seminar 2010 /$fedited by Bertrand Duplantier, Stéphane Nonnenmacher, Vincent Rivasseau 205 $a1st ed. 2013. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (281 p.) 225 1 $aProgress in Mathematical Physics,$x1544-9998 ;$v66 300 $a"... Fourteenth seminar, held on June 5, 2010". 311 $a3-0348-0696-5 320 $aIncludes bibliographical references and index. 327 $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 ?-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?. 330 $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 ?-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. 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. 410 0$aProgress in Mathematical Physics,$x1544-9998 ;$v66 606 $aDynamics 606 $aErgodic theory 606 $aNumber theory 606 $aQuantum field theory 606 $aString theory 606 $aStatistical physics 606 $aDynamical systems 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aQuantum Field Theories, String Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P19048 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aNumber theory. 615 0$aQuantum field theory. 615 0$aString theory. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aNumber Theory. 615 24$aQuantum Field Theories, String Theory. 615 24$aComplex Systems. 615 24$aStatistical Physics and Dynamical Systems. 676 $a003.857 676 $a515.39 702 $aDuplantier$b Bertrand$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aNonnenmacher$b Stéphane$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aRivasseau$b Vincent$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910437864003321 996 $aChaos$91080195 997 $aUNINA