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Quantum chaos. An introduction. (English) Zbl 0940.81019
Cambridge: Cambridge University Press. x, 368 p. (1999).
The monograph arose from lecture series on quantum mechanics of classically chaotic systems. Its attitude is conspicuously pedagogical, specifically while introducing mathematical concepts of the random matrix theory, quantum behaviour of billiard systems and periodic orbit calculations of spectra. The book does not advance any novel mathematics but should be recommended to those interested in experimental and generally-physical concepts that underlie the so-called quantum chaos.
Experiments on Chladni figures, microwave billiards, mesoscopic structures (quantum dots, wells and corrals) are supplemented by a number of numerical examples. The book appears to be more accessible to non-experts than the monographs by F. Haake [Quantum signatures of chaos. Springer, Berlin (1991; Zbl 0741.58055) or M. C. Gutzwiller [Chaos in classical and quantum mechanics. Springer, New York (1990; Zbl 0727.70029)]. For experts on classically ergodic systems and related (quantum) eigenvalue problems for Laplacians on Riemannian manifolds, the book may be a nice conceptual introduction to physical problems that underlie more advanced mathematical research by V. F. Lazutkin [KAM theory and semiclassical approximations to eigenfunctions. Springer, Berlin (1993; Zbl 0814.58001)] or I. Chavel [Eigenvalues in Riemannian geometry. Academic Press, Orlando (1984; Zbl 0551.53001)]. An alternative exposition of mesoscopic systems is given by N. E. Hurt [Quantum chaos and mesoscopic systems. Kluwer, Dordrecht (1997; Zbl 0895.58048)].

MSC:
81Q50 Quantum chaos
81-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
35J25 Boundary value problems for second-order elliptic equations
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