Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner’s reaction matrix for irregular graphs with absorption

Abstract

We present the results of an experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner reaction K matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modeled by optical potentials. The distribution of the reflection coefficient P(R) and the distributions of the reaction K matrix were obtained from measurements and numerical calculations of the scattering matrix S of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory.

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

“…Accordingly, the fluctuation properties in the spectra of classically chaotic quantum graphs with and without T invariance are expected to coincide with those of random matrices from the GOE and the GUE, respectively. This was confirmed experimentally [10,11] for the nearest-neighbor spacing distribution using microwave networks [22][23][24][25][26].…”

“…The effects of T violation on the spectral properties of the eigenvalues of closed quantum systems have also been investigated in such systems [35][36][37]. However, it is difficult if not impossible to obtain complete T violation in microwave billiards, whereas its achievement is straightforward in microwave networks [22][23][24][25][26].…”

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

“…In physics, quantum graphs have been used to model many phenomena, such as acoustic and electromagnetic waveguide networks, quantum Hall systems and mesoscopic quantum systems [1]. Researchers have studied quantum graphs experimentally and numerically [3][4][5][6]. Quantum graphs have been realized as microwave networks with different topologies such as tetrahedral, irregular hexagon fully connected networks, and fully connected five vertex networks [3][4][5][6].…”

“…Researchers have studied quantum graphs experimentally and numerically [3][4][5][6]. Quantum graphs have been realized as microwave networks with different topologies such as tetrahedral, irregular hexagon fully connected networks, and fully connected five vertex networks [3][4][5][6]. Spectral statistics of graph systems [3,5], the statistics of the reaction matrix K [4,5] and the reflection statistics for one-port graphs [4,5], and the impedance statistics of networks of complex enclosures [7], have been studied and results from both numerical calculation and experimental measurement show good agreement with theory.…”

“…The microwave networks, with bonds that are large compared with the wavelength, are constructed from coaxial cables connected by T junctions [3][4][5][6]. The graph is open with two coupled ports.…”