PROGRAMA



QUANTUM CHAOS AND SEMICLASSICAL METHODS

1.-	Introduction	Information-theoretic view of dynamical systems; asymptotic relations between theories.
2.-	Hamiltonian dynamics	Integrability; tori; canonical perturbation theory; small denominators; Kolmogorov-Arnol'd-Moser theorem; Poincaré-Birkhoff theorem.
3.-	Measures and levels of chaoticity	Lyapunov exponent; Kolmogorov-Sinai entropy; ergodic, mixing, hyperbolic systems; K-Systems; C-systems; Bernoulli shifts; hierarchy of chaoticity.
4.-	Some pertinent examples	Bernoulli map; baker map; cat map; kicked rotor; billiards.
5.-	Semiclassical approximations	EBK quantization; WKB quantization; turning-point problem; caustics; connection formulae; van-Vleck propagator; Gutzwiller's trace formula; scars.
6.-	Phase-space dynamics	Liouville dynamics; classical Hilbert space; invariant sets and measures; Lagrangian manifolds; Wigner function; coherent states; Husimi function.
7.-	Spectral statistics	Spectral density; spectral correlations; random-matrix theory; relation spectrum--dynamics; semiclassical approach to random-matrix theory.

BIBLIOGRAPHY

BOOKS

Alfredo M.Ozorio de Almeida: "Hamiltonian Systems: Chaos and Quantization", Cambridge Monographs on Mathematical Physics, Cambridge University Press (Cambridge, 1988).

Martin C. Gutzwiller: "Chaos in Classical and Quantum Dynamics", Interdisciplinary Applied Mathematics, vol. 1, Springer (New York, 1990).

Fritz Haake: "Quantum Signatures of Chaos", Springer Series in Synergetics, vol. 54, Springer (Berlin, 1991).

Linda E. Reichl: "The Transition to Chaos: In Conservative Systems: Quantum Manifestations", Institute for Nonlinear Science, vol. 2, Springer (New York, 1992).

Edward Ott: "Chaos in Dynamical Systems", Cambridge University Press (Cambridge, 1993).

Allan J. Lichtenberg and Michael A. Lieberman: "Regular and Stochastic Motion", 2nd ed., Applied Mathematical Sciences, vol. 38, Springer (New York, 1992).

Wolfgang P. Schleich: "Quantum Optics in Phase Space", Wiley--VCH (Berlin, 2001).

Madan L. Mehta: "Random Matrices", 2nd ed., Academic Press (San Diego, 1991).

REVIEW ARTICLES

Michael V. Berry: "Semiclassical Aspects of Regular and Chaotic Motion", in "Chaotic Behaviour of Deterministic Systems", G. Iooss, R. H. G. Helleman, and G. Stora (eds.), Les Houches Lectures XXXVI, North-Holland (Amsterdam, 1983).

Thomas Dittrich: "Chaos, Coherence, and Dissipation", in "Quantum Transport and Dissipation", T. Dittrich et al., Wiley-VCH (Weilheim, 1998).