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

Electromagnetic prompt response in an elastic wave cavity

A rapid, or prompt response, of an electromagnetic nature, is found in an elastic wave scattering experiment. The experiment is performed with torsional elastic waves in a quasi-one-dimensional cavity with one port, formed by a notch grooved at a certain distance from the free end of a beam. The stationary patterns are diminished using a passive vibration isolation system at the other end of the beam. The measurement of the resonances is performed with non-contact electromagnetic-acoustic transducers outside the cavity. In the Argand plane, each resonance describes a circle over a base impedance curve which comes from the electromagnetic components of the equipment. A model, based on a variation of Poisson's kernel is developed. Excellent agreement between theory and experiment is obtained.Comment: 4 pages, 5 figure

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

Experimental determination of the absorption strength in absorbing chaotic cavities

Due to the experimental necessity we present a formula to determine the absorption strength by power losses inside a chaotic system (cavities, graphs, acoustic resonators, etc) when the antenna coupling, always present in experimental measurements, is taken into account. This is done by calculating the average of the absorption coefficient as a function of the absorption strength and the coupling of the antenna to the system, in the one channel case.Comment: 6 pages, 3 figures, Submitted to Phys. Rev.

Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.Comment: Added two appendices and references. Corrected typo