Universal and nonuniversal properties of wave-chaotic scattering systems

Abstract

Prediction of the statistics of scattering in typical wave-chaotic systems requires combining system-specific information with universal aspects of chaotic scattering as described by random matrix theory. This Rapid Communication shows that the average impedance matrix, which characterizes such system-specific properties, can be semiclassically calculated in terms of ray trajectories between ports. Theoretical predictions are compared with experimental results for a microwave billiard, demonstrating that the theory successfully uncovered universal statistics of wave-chaotic scattering systems.

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

“…From the plots, we can see that Z and Zavg are both fluctuating around the slowly-varying Zrad. The small oscillations in Zavg are manifestations of the short-orbits that survive in many realizations of the networks [19]. Resistance and reactance (real and imaginary parts of impedance) of one realization of a tetrahedral graph network (blue, large amplitude fluctuations, labeled Z), averaged impedance over all realizations (red, intermediate amplitude fluctuations, labeled Zavg) and measured radiation impedance (green, smooth curve, labeled Zrad) from 9 to 10 GHz.…”

“…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. In this paper, the RCM is applied for the analysis of electromagnetic propagation in quasi-1D microwave networks.…”

“…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.…”

“…Next, the average of the measured impedance over all these realizations is compiled. This averaged impedance quantity captures both the radiation impedance of the ports and the contributions of short orbits between the ports [11,12]. We then take the measured impedance and normalize it (i.e.…”

Propagation of Current Waves along Randomly Located Multiconductor Transmission Lines inside a Rectangular Resonator

“…For those studies papers of S. Hemmadi and T.M. Antonsen and their groups [1,2] are well known, which are based on a deep investigation of the mathematical properties of stochastic cavities [3], when they investigate the response of components in stochastic cavities. The authors of [4] consider stochastically located small antennas to create stochastic fields in a MSC.…”