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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 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.
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.
"The monograph may be used as a reference book, both for professionals and for teaching purposes. Each chapter is followed by a selection of problem which may be regarded as a test, but also are intended to deepen the reader understanding." (Piotr Garbaczewski, zbMATH 1414.81001, 2019)
From the reviews of the third edition:
"The book can be recommended both as a textbook and a review of the subject. The rich set of references allows one to catch up with the current literature. Exercises facilitate the study and will be of use to the lecturer. It can be a base of a solid graduate theoretical course in quantum chaos." (Pure and Applied Geophysics, 160, 2003)
"In summary, this is definitely an essential reference book for the specialist. It will also ably serve someone entering the field for the first time who needs to learn the theoretical state of the art in detail." (G. Summy (University of Oxford), Contemporary Physics 2002, vol. 43, page 232)
"This book is about aspects of quantum chaos, with emphasis on energy-level statistics ... and their relation to random matrix theory, including a self-contained introduction to the supersymmetric technique, as well as semiclassical periodic-orbit expansions. ... Each chapter ends with a list of problems and references, which is helpful to the specialist and the beginner as well." (César R. de Oliveira, Mathematical Reviews, Issue 2011 d)
"This book is phenomenal and brings many topics Quantum Chaos who were treated in a sovereign manner by Fritz Haake. Thus I recommend this book for anyone who is interested in the study of the distribution of eigenvalues of generic operators, especially those related to quantum problems. It is an essential book for any researcher in Quantum Chaos, sometimes this book is known as the Quantum Chaos 'bible'." (Philosophy, Religion and Science Book Reviews, September, 2012)
"This by now classic text ... witnesses both the rapid growth of a new field of 'quantum chaology' and its subsequent maturity period plus further developments. ... Each chapter is accompanied by a selection of problems which both test and deepen the reader understanding of the material presented. The text is both an introduction and asurvey of the field of quantum chaos. References to original research papers direct the reader to more advanced discussion of topics that were outlined in the present text." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1209, 2011)
"The book can be recommended both as a textbook and a review of the subject. The rich set of references allows one to catch up with the current literature. Exercises facilitate the study and will be of use to the lecturer. It can be a base of a solid graduate theoretical course in quantum chaos." (Pure and Applied Geophysics, 160, 2003)
"In summary, this is definitely an essential reference book for the specialist. It will also ably serve someone entering the field for the first time who needs to learn the theoretical state of the art in detail." (G. Summy (University of Oxford), Contemporary Physics 2002, vol. 43, page 232)
"This book is about aspects of quantum chaos, with emphasis on energy-level statistics ... and their relation to random matrix theory, including a self-contained introduction to the supersymmetric technique, as well as semiclassical periodic-orbit expansions. ... Each chapter ends with a list of problems and references, which is helpful to the specialist and the beginner as well." (César R. de Oliveira, Mathematical Reviews, Issue 2011 d)
"This book is phenomenal and brings many topics Quantum Chaos who were treated in a sovereign manner by Fritz Haake. Thus I recommend this book for anyone who is interested in the study of the distribution of eigenvalues of generic operators, especially those related to quantum problems. It is an essential book for any researcher in Quantum Chaos, sometimes this book is known as the Quantum Chaos 'bible'." (Philosophy, Religion and Science Book Reviews, September, 2012)
"This by now classic text ... witnesses both the rapid growth of a new field of 'quantum chaology' and its subsequent maturity period plus further developments. ... Each chapter is accompanied by a selection of problems which both test and deepen the reader understanding of the material presented. The text is both an introduction and asurvey of the field of quantum chaos. References to original research papers direct the reader to more advanced discussion of topics that were outlined in the present text." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1209, 2011)