Overview
- Completely revised and modernized 4th edition of a classic text
- Expands further on the supersymmetric sigma model and its applications
- Provides end-of-chapter problems throughout
Part of the book series: Springer Series in Synergetics (SSSYN)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Quantum Signatures of Chaos
Authors: Fritz Haake, Sven Gnutzmann, Marek Kuś
Series Title: Springer Series in Synergetics
DOI: https://doi.org/10.1007/978-3-319-97580-1
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-97579-5Published: 28 February 2019
eBook ISBN: 978-3-319-97580-1Published: 18 February 2019
Series ISSN: 0172-7389
Series E-ISSN: 2198-333X
Edition Number: 4
Number of Pages: XXVI, 659
Number of Illustrations: 78 b/w illustrations, 18 illustrations in colour
Topics: Quantum Physics, Applications of Nonlinear Dynamics and Chaos Theory, Statistical Physics and Dynamical Systems, Mathematical Methods in Physics