Structural Invariance and the Energy Spectrum

We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the semiclassical limit, is extended to the energy spectra of bounded time independent systems. We proceed by showing that the results obtained previously for the quasi-energies and eigenphases of the S-matrix can be extended to the eigenphases of the quantum Poincare map which is unitary in the semiclassical limit. We then show that its eigenphases in the chaotic case move rather stiffly around the unit circle and thus their local statistical fluctuations transfer to the energy spectrum via Bogomolny's prescription. We verify our results by studying numerically the properties of the eigenphases of the quantum Poincare map for billiards by using the boundary integral method.Comment: 10 pages, 5 figure

Dynamical properties of a dissipative discontinuous map: A scaling investigation

The effects of dissipation on the scaling properties of nonlinear discontinuous maps are investigated by analyzing the behavior of the average squared action \left as a function of the $n$-th iteration of the map as well as the parameters $K$ and $\gamma$, controlling nonlinearity and dissipation, respectively. We concentrate our efforts to study the case where the nonlinearity is large; i.e., $K\gg 1$. In this regime and for large initial action $I_0\gg K$, we prove that dissipation produces an exponential decay for the average action \left. Also, for $I_0\cong 0$, we describe the behavior of \left using a scaling function and analytically obtain critical exponents which are used to overlap different curves of \left onto an universal plot. We complete our study with the analysis of the scaling properties of the deviation around the average action $\omega$.Comment: 20 pages, 7 figure

Anderson Localization Phenomenon in One-dimensional Elastic Systems

The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the re ection coefficient of a single scatterer in each case.Comment: 15 pages, 10 figure

The relation between bar formation, galaxy luminosity, and environment

We derive the bar fraction in three different environments ranging from the field to Virgo and Coma clusters, covering an unprecedentedly large range of galaxy luminosities (or, equivalently, stellar masses). We confirm that the fraction of barred galaxies strongly depends on galaxy luminosity. We also show that the difference between the bar fraction distributions as a function of galaxy luminosity (and mass) in the field and Coma cluster are statistically significant, with Virgo being an intermediate case. We interpret this result as a variation of the effect of environment on bar formation depending on galaxy luminosity. We speculate that brighter disk galaxies are stable enough against interactions to keep their cold structure, thus, the interactions are able to trigger bar formation. For fainter galaxies the interactions become strong enough to heat up the disks inhibiting bar formation and even destroying the disks. Finally, we point out that the controversy regarding whether the bar fraction depends on environment could be resolved by taking into account the different luminosity ranges of the galaxy samples studied so far.Comment: 4 pages, 2 figures. To appear in the proceedings of EWASS 2012 Special Session 4, Structure of galaxy disks shaped by secular evolution and environmental processes, ed. P. Di Matteo and C. Jog, Memorie della Societ\`a Astronomica Italiana Supplement Serie