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Record Nr. |
UNINA9910311936303321 |
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Autore |
Haake Fritz |
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Titolo |
Quantum Signatures of Chaos / / by Fritz Haake, Sven Gnutzmann, Marek Kuś |
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Pubbl/distr/stampa |
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Cham : , : Springer International Publishing : , : Imprint : Springer, , 2018 |
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ISBN |
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Edizione |
[4th ed. 2018.] |
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Descrizione fisica |
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1 online resource (XXVI, 659 p. 96 illus., 18 illus. in color.) |
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Collana |
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Springer Series in Synergetics, , 0172-7389 |
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Disciplina |
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Soggetti |
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Quantum theory |
Statistical physics |
Physics |
Quantum Physics |
Applications of Nonlinear Dynamics and Chaos Theory |
Statistical Physics and Dynamical Systems |
Mathematical Methods in Physics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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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. . |
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Sommario/riassunto |
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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 |
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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. |
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