**Projects**

## 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.