Characterization of fluctuations of impedance and scattering matrices in wave chaotic scattering

Abstract

In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, V Rz and V Rs, where, and V ar[.] denotes variance. V Rz is shown to be a universal function of distributed losses within the scatterer. That is, V Rz is independent of nonuniversal coupling details. This contrasts with V Rs for which universality applies only in the large loss limit. Explicit results are given for V Rz for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.

Source Correlation in Randomly Excited Complex Media

“…The general representation in (9) does not allow to push this idea further, as the double dependence of the coupling dyad on r and r ′ corresponds to a spatial-variant filtering; in other words, (9) is not equivalent to a convolution integral. This would be the case only if…”

“…As a result, the modal coefficients will be statistically correlated, thus reducing the actual number of degrees of freedom potentially provided by the medium, on average. A quantitative evaluation of (9) in this case will generally require a numerical approach, so that it is hardly possible to make any broad prediction, particularly because of the strong sensitivity that can be expected on the details of the configuration of interest.…”

“…Statistical models are typically proposed to reproduce the behavior of the electromagnetic fields thus generated, e.g., by representing the fields as continuous stochastic processes [2], [3], [4], [5] or by representing the propagation through a superposition of contributions modulated by random coefficients [6], [7], [8], [9]. The rationale for approximating the fields as random variables is not only based on the complexity of the wave propagation, but also on the existence of further randomizing processes, such as the presence of moving scatterers or even in the case of a static medium where the sources are randomly positioned, e.g., in the case of channel fading [10].…”

Experimental Study of Quantum Graphs with Simple Microwave Networks: Non-Universal Features

“…The RCM gives a prescription for determining both the universal and non-universal features of the experiment. The RCM has successfully analyzed the statistical properties of the impedance ( Z) and scattering ( S) matrices of open electromagnetic cavities where the waves are coupled through transmission lines or waveguide [13]. In [11,14], a 2D ray-chaotic quarter-bowtie cavity and in [16] a 3D complex "GigaBox" cavity have been studied and impedance statistics have been analyzed from experimental measurement.…”

“…remove the effects of the port radiation impedances and short orbits) to examine a fluctuating impedance. In the case of wave chaotic systems it is expected that the normalized impedance has a probability density function (PDF) that is described by Random Matrix Theory (RMT), and this PDF is governed by a single parameter, namely the loss parameter α [11][12][13][14]. In principle, one can then fit the normalized impedance (real and imaginary) data PDFs to RMT and determine α as a fitting parameter.…”