LEADER 04019nam 22005775 450 001 9910311936303321 005 20251116212035.0 010 $a3-319-97580-3 024 7 $a10.1007/978-3-319-97580-1 035 $a(CKB)4100000007656730 035 $a(DE-He213)978-3-319-97580-1 035 $a(MiAaPQ)EBC5716809 035 $a(PPN)235004367 035 $a(EXLCZ)994100000007656730 100 $a20190218d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum Signatures of Chaos /$fby Fritz Haake, Sven Gnutzmann, Marek Ku? 205 $a4th ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXVI, 659 p. 96 illus., 18 illus. in color.) 225 1 $aSpringer Series in Synergetics,$x0172-7389 311 08$a3-319-97579-X 327 $aIntroduction -- Time Reversal and Unitary Symmetries -- Level Repulsion -- Level Clustering -- Random-Matrix Theory -- Supersymmetry and Sigma Model for Random Matrices -- Ballistic Sigma Model for Individual Unitary Maps and Graphs -- Quantum Localization -- Classical Hamiltonian Chaos -- Semiclassical Roles for Classical Orbits -- Level Dynamics -- Dissipative Systems. . 330 $aThis by now classic text provides an excellent introduction to and survey of the still-expanding field of quantum chaos. For this long-awaited fourth edition, the original text has been thoroughly modernized. The topics include a brief introduction to classical Hamiltonian chaos, a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria used to distinguish regular and irregular motion, and antiunitary (generalized time reversal) and unitary symmetries. The standard Wigner-Dyson symmetry classes, as well as the non-standard ones introduced by Altland and Zirnbauer, are investigated and illustrated with numerous examples. Random matrix theory is presented in terms of both classic methods and the supersymmetric sigma model. The power of the latter method is revealed by applications outside random-matrix theory, such as to quantum localization, quantum graphs, and universal spectral fluctuations of individual chaotic dynamics. The equivalence of the sigma model and Gutzwiller?s semiclassical periodic-orbit theory is demonstrated. Last but not least, the quantum mechanics of dissipative chaotic systems are also briefly described. Each chapter is accompanied by a selection of problems that will help newcomers test and deepen their understanding, and gain a firm command of the methods presented. 410 0$aSpringer Series in Synergetics,$x0172-7389 606 $aQuantum theory 606 $aStatistical physics 606 $aPhysics 606 $aQuantum Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19080 606 $aApplications of Nonlinear Dynamics and Chaos Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/P33020 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 615 0$aQuantum theory. 615 0$aStatistical physics. 615 0$aPhysics. 615 14$aQuantum Physics. 615 24$aApplications of Nonlinear Dynamics and Chaos Theory. 615 24$aStatistical Physics and Dynamical Systems. 615 24$aMathematical Methods in Physics. 676 $a530.12 700 $aHaake$b Fritz$4aut$4http://id.loc.gov/vocabulary/relators/aut$063008 702 $aGnutzmann$b Sven$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aKu?$b Marek$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910311936303321 996 $aQuantum signatures of chaos$9374229 997 $aUNINA