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**Quantum signatures of chaos.
2nd rev. and enlarged ed.**
*(English)*
Zbl 0985.81038

Berlin: Springer. xx, 460 p. (2001).

The second edition of this monograph almost twice exceeds in volume the first one (1991; Zbl 0741.58055). The rapid development of the field of quantum chaos has been captured by rewriting the previous material and including some important progress made during the decade.

With respect to the considerable theoretical physics research, the book focuses on the deeper statistical exploitation of level dynamics, improved control of semiclassical periodic-orbit expansions, and superanalytic techniques for dealing with various types of random matrices. Those three fields, in conjunction, contribute to an understanding ???? certain spectral fluctuations in classically nonintegrable systems are universal and ???? there are exceptions.

The author himself warns that even within this large volume (497 pp) important and interesting material has to be left out (specifically an issue of chaotic scattering systems with mixed phase spaces, experimental advances).

The monograph may be utilized as a textbook. The topics include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish regular and irregular motion, an account of time reversal and (anti)unitary symmetries, plus an extended discussion of quantum dissipative systems. Each chapter is accompanied by a list of problems.

With respect to the considerable theoretical physics research, the book focuses on the deeper statistical exploitation of level dynamics, improved control of semiclassical periodic-orbit expansions, and superanalytic techniques for dealing with various types of random matrices. Those three fields, in conjunction, contribute to an understanding ???? certain spectral fluctuations in classically nonintegrable systems are universal and ???? there are exceptions.

The author himself warns that even within this large volume (497 pp) important and interesting material has to be left out (specifically an issue of chaotic scattering systems with mixed phase spaces, experimental advances).

The monograph may be utilized as a textbook. The topics include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria to distinguish regular and irregular motion, an account of time reversal and (anti)unitary symmetries, plus an extended discussion of quantum dissipative systems. Each chapter is accompanied by a list of problems.

Reviewer: Piotr Garbaczewski (Zielona Gora)

### MSC:

81Q50 | Quantum chaos |

81-02 | Research exposition (monographs, survey articles) pertaining to quantum theory |

81Q60 | Supersymmetry and quantum mechanics |