Absorption and Direct Processes in Chaotic Wave Scattering

Recent results on the scattering of waves by chaotic systems with losses and direct processes are discussed. We start by showing the results without direct processes nor absorption. We then discuss systems with direct processes and lossy systems separately. Finally the discussion of systems with both direct processes and loses is given. We will see how the regimes of strong and weak absorption are modified by the presence of the direct processes.Comment: 8 pages, 4 figures, Condensed Matter Physics (IV Mexican Meeting on Mathematical and Experimental Physics), Edited by M. Martinez-Mares and J. A. Moreno-Raz

Anderson Localization in Disordered Vibrating Rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.Comment: 10 pages, 6 figure

Deep spectroscopic luminosity function of Abell 85: no evidence for a steep upturn of the faint-end slope

We present a new deep determination of the spectroscopic LF within the virial radius of the nearby and massive Abell\,85 (A85) cluster down to the dwarf regime (M* + 6) using VLT/VIMOS spectra for $\sim 2000$ galaxies with m$_r \leq 21$ mag and $\langle \mu_{e,r} \rangle \leq 24$ mag arcsec$^{-2}$. The resulting LF from 438 cluster members is best modelled by a double Schechter function due to the presence of a statistically significant upturn at the faint-end. The amplitude of this upturn ($\alpha_{f} = -1.58^{+0.19}_{-0.15}$), however, is much smaller than that of the SDSS composite photometric cluster LF by Popesso et al. 2006, $\alpha_{f} \sim$ -2. The faint-end slope of the LF in A85 is consistent, within the uncertainties, with that of the field. The red galaxy population dominates the LF at low luminosities, and is the main responsible for the upturn. The fact that the slopes of the spectroscopic LFs in the field and in a cluster as massive as A85 are similar suggests that the cluster environment does not play a major role in determining the abundance of low-mass galaxies.Comment: 6 pages, 4 figures, accepted at MNRAS lette

Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment

We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall