04019nam 22005775 450 991031193630332120251116212035.03-319-97580-310.1007/978-3-319-97580-1(CKB)4100000007656730(DE-He213)978-3-319-97580-1(MiAaPQ)EBC5716809(PPN)235004367(EXLCZ)99410000000765673020190218d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierQuantum Signatures of Chaos /by Fritz Haake, Sven Gnutzmann, Marek Kuś4th ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XXVI, 659 p. 96 illus., 18 illus. in color.) Springer Series in Synergetics,0172-73893-319-97579-X Introduction -- 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. .This 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.Springer Series in Synergetics,0172-7389Quantum theoryStatistical physicsPhysicsQuantum Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19080Applications of Nonlinear Dynamics and Chaos Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/P33020Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Quantum theory.Statistical physics.Physics.Quantum Physics.Applications of Nonlinear Dynamics and Chaos Theory.Statistical Physics and Dynamical Systems.Mathematical Methods in Physics.530.12Haake Fritzauthttp://id.loc.gov/vocabulary/relators/aut63008Gnutzmann Svenauthttp://id.loc.gov/vocabulary/relators/autKuś Marekauthttp://id.loc.gov/vocabulary/relators/autBOOK9910311936303321Quantum signatures of chaos374229UNINA