Quantum Signatures of Chaos: 54 3rd ed. 2010 Edition

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 a survey 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)

This by now classic text provides an excellent introduction and survey to the continuously expanding field of quantum chaos . The topics treated include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish regular and irregular motion, antiunitary symmetries (generalized time reversal), random matrix theory and a thorough account of the quantum mechanics of dissipative systems. Each chapter is accompanied by a selection of problems which will help the newcomer to test and deepen his/her understanding and to acquire an active command of the methods presented.

In addition to a significant number of smaller revisions and chapter updates, the third edition thoroughly expands on the understanding of universal spectral fluctuations, and to subsequently make the presentation of all semi-classical developments self-contained – a new chapter on classical Hamiltonian chaos has been inserted.

From the reviews of the 2^nd edition: 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, p 232)