Book review:Chaotic behavior in quantum systems

The concept of chaos, as its use has evolved in the theory of dynamic systems, has crept ever closer to that of random or stochastic. Among the general characteristics associated with chaos have been the sensitive dependence on initial conditions and the loss of predictability. Chaos is a phenomenon that appears in both conservative nonintegrable Hamiltonian systems (KAM theory, tori breakdown, etc.) and nonconservative dissipative systems (strange attractors, noninvertible maps, etc.). The richness of the structures generated by nonlinear interactions in classical systems has led a number of scientists to inquire how these phenomena are instantiated in the quantum domain. Surely the nonlinear interaction term in a classically nonintegrable Hamiltonian system should manifest new behavior in its quantum counterpart; at least an ever-growing segment of the scientific community believes this to be the case. The spectrum of presentations at the conference was quite broad, ranging from the limitations of perturbation theory, where the small divisor problem plagued astronomers and may also lead to strong energy resonances to produce quantum tunneling, to torus quantization, to Anderson localization, to the fluctuations in nuclear spectra. Although not of uniform mathematical difficulty, there was a sufficient breadth of mathematical topics in the lectures to challenge the background of most mathemtical physicists. The fundamenal physical problem was to find criteria to characterize quantum chaos and the range of suggested criteria highlighted the conjectural aspect of much of the research being described. This state of affairs could cause one to scoff at what is presently understood about quantum chaos or in constrast to stimulate one to investigate this unsettled field still further, depending on one's ability to deal with ambiguity and uncertainty. If numbers are any indication, it would seem that studies into the foundations of quantum mechanics are undergoing a rebirth. I recommend these lectures to anyone who has ever wondered what