The main purpose of this
project is to investigate theoretically, and experimentally, many aspects
of quantum chaos. We shall study the vibrations of classical systems whose
eigenmodes simulate the eigenstates of some corresponding quantum system.
A fundamental part of this program is the creation of a laboratory for
measuring the resonance frequencies of the acoustic waves excited in blocks
or plates of various materials (aluminum, quartz, ceramic, etc.). Acoustic
resonators, due to the high quality of data provided by them, are ideal
experimental devices for testing many of the existing predictions about
spectra and wavefunctions. Topics that will be investigated within this
context are: intermediate statistics for random matrix theory and its classical
analog, symmetry breaking in complex systems, chaotic acoustic billiards,
universality in parametric level motion, chaos in nuclei, and Anderson
localization, etc.
Over the last decade, there
have been important activities in different areas of nonlinear physics
at the Instituto de Física da Universidade de São Paulo-IFUSP.
The physicists that are presenting this research proposal, Maurício
Porto Pato, Mahir Saleh Hussein, Coraci Pereira Malta and José Carlos
Sartorelli are amongst the most active in this field.
Maurício Porto Pato and Mahir Saleh Hussein collaborate with local researchers or from important institutions abroad, concentrating their efforts in the study of the manifestation of chaos in quantum systems. Their major contribution has been the development of statistical models based on ensembles of random matrices and their application to a wide gamma of systems from Nuclear to Condensed Matter Physics. They are now the Brazilian partners of a Cooperation CNPq/NSF, in which they participate as theoreticians in experiments at the Triangle University National Laboratory (TUNL) on symmetry violation in quantum many-body systems.
Coraci Pereira Malta has been working in various aspects of the theory of dynamical systems. She has investigated the quantum signature of a period-doubling bifurcation (in the semiclassical limit) for a system whose classical analog is described by a non-integrable 2-degree of freedom Hamiltonian. The main periodic families of the classical system produce strong scars in the wave intensities. She has also developed with her group of collaborators a great skill in dealing with numerical calculations in nonlinear problems with application in biological problems.
José Carlos Sartorelli has created in 94 at the IFUSP the Laboratory of Nonlinear Phenomena to study the chaotic behavior of nonlinear classical dynamical systems. The first experiment assembled at the laboratory aimed to study the dynamics of water drop formation in dripping faucets. It has already produced many results.
The main purpose of this project
is to combine the expertise of these physicists in a common research program
aiming an experimental and theoretical investigation of many aspects of
quantum chaos. Their aim is to study vibrations of classical physical systems
whose eigenmodes simulate eigenstate properties of some corresponding quantum
system. In the last years, this idea has been implemented with great success
by important experimental groups in Europe and also in USA. There are two
kinds of classical sytems having quantum analogous systems which have been
studied. One is the microwave oscillations in electromagnetic cavities
and the other is the elastomechanical vibrations of acoustic resonators.
We have decided to do experiments on this last kind of systems based mainly
on their lower cost. Nevertheless, and we stress this, as classical systems
that have not been completely understood yet, they constitute interesting
physical problems themselves. It has been already tested with excellent
results by the experimentalgroup of
Chaos and Turbulence Studies (CATS) of the Niels Bohr Institute in Copenhagen.
A preliminary collaboration with this group is allowing us to count with
their know-how in the preparation of this project.
2. Coraci Pereira Malta, Associate Professor, Depto. de Física Nuclear, Instituto de Física, USP.
3.José Carlos Sartorelli Associate Professor, Depto. de Física, Instituto de Física, USP.
4. Mahir Saleh Hussein, Professor of Physics, Depto. de Física Nuclear, Instituto de Física, USP.
6. Élcio Abdalla, Professor of Physics, IF - USP.
7. Clodoaldo Grotta-Ragazzo, Associate Professor, Instituto de Matemática e Estatística - USP.
8. Marcus A. M. de Aguiar, Associate Professor, Instituto de Física Gleb Wataghin, UNICAMP.
9. Maria Carolina Nemes, Professor of Physics, Instituto de Física, UFMG.
10. Clive Ellegard, Niels Bohr Institute, Copenhagen, Denmark.
11. Gary Mitchell, North Carolina State University,
Dept. of Physics and Triangle Universities Nuclear Laboratory, USA.
C. Y-Lin
O. K. Vorov
A. Sargeant
M. Ueda
Kristian Schaadt