%0 Book Section %1 statphys23_0672 %A Sartorelli, J.C. %A Nogueira, T.N. %A Pato, M.P. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K acoustic chaos quantum resonators statphys23 topic-5 %T Missing level models to describe acoustic resonators experimental data. %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=672 %X The acoustic resonators were supposed to be a classical equivalent of a quantum system for experimental studies of quantum chaos. The experimental NND (nearest neighbor spacing distribution, $\sim4000$ eigenfrequecies) and the spectral rigidity (SR) of an aluminum 1/4 circle plate acoustic resonator presents deviations from the expected behavior of integral systems. The experimental NND is not a Poisson neither a Wigner (1GOE) nor a semi-Poisson distribution. We could reproduce the NND and the SR by simulations in which we rejected one of the frequencies when two successive ressonances were not considered resolved according to the experimental Q ($\sim10^4$) value. For non-integral systems as the Sinai Stadium, a retangle triangle and a scalene one, the experimental NNDs ($1000$ eigenfrequencies) are reasonable described by the Wigner distribution (1GOE), but the SR data are not described by the 1GOE prediction. In these cases, there is levels repulsion and the resolution should not be the main source of missing levels. By supposing that a fraction of the resonances can be too weak to be experimentally observed we applied the missing levels Bohigas & Pato model, in which $\sim$5\% of the eigenfrequencies were rejected randomly. In this way, there are no appreciable deviations from the Wigner NND, but the SR simulations can now reproduce the experimental data.

@incollection{statphys23_0672, abstract = {The acoustic resonators were supposed to be a classical equivalent of a quantum system for experimental studies of quantum chaos. The experimental NND (nearest neighbor spacing distribution, $\sim4000$ eigenfrequecies) and the spectral rigidity (SR) of an aluminum 1/4 circle plate acoustic resonator presents deviations from the expected behavior of integral systems. The experimental NND is not a Poisson neither a Wigner (1GOE) nor a semi-Poisson distribution. We could reproduce the NND and the SR by simulations in which we rejected one of the frequencies when two successive ressonances were not considered resolved according to the experimental Q ($\sim10^4$) value. For non-integral systems as the Sinai Stadium, a retangle triangle and a scalene one, the experimental NNDs ($\sim 1000$ eigenfrequencies) are reasonable described by the Wigner distribution (1GOE), but the SR data are not described by the 1GOE prediction. In these cases, there is levels repulsion and the resolution should not be the main source of missing levels. By supposing that a fraction of the resonances can be too weak to be experimentally observed we applied the missing levels Bohigas \& Pato model, in which $\sim$5\% of the eigenfrequencies were rejected randomly. In this way, there are no appreciable deviations from the Wigner NND, but the SR simulations can now reproduce the experimental data.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Sartorelli, J.C. and Nogueira, T.N. and Pato, M.P.}, biburl = {https://www.bibsonomy.org/bibtex/254d895e7b1cd5ba77f05937df87ffc5d/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0dca804032e3513837037b83ccbf80cb}, intrahash = {54d895e7b1cd5ba77f05937df87ffc5d}, keywords = {acoustic chaos quantum resonators statphys23 topic-5}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Missing level models to describe acoustic resonators experimental data.}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=672}, year = 2007 }