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Quantum maps

Quantum maps provide the simplest, yet highly non-trivial, arena for the investigation of the quantum properties of chaotic systems. As simple models of Poincare sections of realistic Hamiltonians or of time dependent "kicked" systems, they provide a testing ground for semiclassical approximations, correlations, universalities, localization, etc.
We have developed techniques for the construction, semiclassical behaviour and phase space description of the baker's map, the Smale horseshoe, cat maps,etc.

Quantum billiards

Billiards in 2-D provide some of the best realistic models where wave and particle behaviour can be studied and related. Besides their intrinsic theoretical interest they describe the behaviour of ballistic electrons in mesoscopic cavities or of light in optical microcavities.
The group has studied extensively the highly excited spectrum of plane chaotic billiards and its semiclassical description in terms of periodic orbits. A very efficient "scaling" method for the precise calculation of very excited eigenstates hasbeen developed, wich is now the best available.
A theory of short periodic orbits is under active development with aim of taming the exponential increase in the number of periodic orbits needed for the semiclassical description of spectral properties.

Quantum algorithms

In collaboration with J. P. Paz at the Phys. Dep. of the Univ. of Buenos Aires, we are studying quantum algorithms viewed as quantum maps. Thus, we can apply semiclassical techniques, phase space analysis, and long time behaviour characteristics of quantum maps to the operation of quantum circuits, providing a novel approach in this area.

Transport phenomena in mesoscopic systems

This program is developed in collaboration with A. Fendrik and M.J. Sanchez at the Physics Department (University of Buenos Aires) and aims at the application of the general methods of chaotic dynamics to the study of mesoscopic systems. We have studied persistent currents and the effects of surface roughness in ballistic cavities and the statistical properties of the fluctuations in the total energy in a non interacting fermion system.

Chaotic scattering at the nuclear coulomb barrier

There are interesting and characteristic anomalies in the heavy ion cross sections and angular distributions at backwards angles that can be interpreted as arising from chaotic scattering due to the coupling of intrinsic and translational degrees of freedom at Coulomb barrier energies. We have modeled these processes and proposed experiments to test these characteristics.