Experimental Investigation of Reflection Coefficient and Wigner's Reaction Matrix for Microwave Graphs

Abstract

We present the results of experimental study of the distribution P (R) of the reflection coefficient R and the distributions of Wigner's reaction K matrix for irregular, tetrahedral microwave graphs (networks) in the presence of absorption. Our experimental results are in good agreement with the exact theoretical predictions of Savin et al.

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

“…In the case of time reversal systems (symmetry index β = 1) P (R) has been studied experimentally by Méndez-Sánchez et al [35]. The distributions P (v) and P (u) have been studied for chaotic microwave cavities in [26,36] and for microwave networks for moderate absorption strength γ ≤ 7.1 in [22,23]. For systems without time reversal symmetry (β = 2) and a single perfectly coupled channel P (R) was calculated by Beenakker and Brouwer [37] while the exact formulas for the distributions P (v) and P (u) were given by Fyodorov and Savin [25].…”

“…From the experimental point of view absorption of the networks can be changed by the change of the bonds' (cables') lengths [21] or more effectively by the application of microwave attenuators [22,23]. In the numerical calculations weak absorption inside the cables can be described with the help of complex wave vector [21].…”

“…Recently it has been shown that quantum graphs are excellent paradigms of quantum chaos [11,12,13,14,15,16,17,18,19,20,21]. More complicated and thus more realistic systems -microwave networks with moderate absorption strength γ = 2πΓ/∆ ≤ 7.1, where Γ is the absorption width and ∆ is the mean level spacing, have been experimentally investigated in [22,23]. Other interesting open objects -quantum graphs with leads -have been analyzed in details in [14,15].…”

“…The distribution P (R) of the reflection coefficient R and the distributions of the imaginary and real parts of the Wigner's reaction matrix K for microwave networks with absorption were found using the impedance approach [23,26,36]. In this approach the real and imagi-…”

Experimental and Numerical Studies of One-Dimensional and Three-Dimensional Chaotic Open Systems

“…Quantum graphs with absorption, more realistic but more complicated systems, have been recently studied in [16,17,[23][24][25]. The distribution of the reflection coefficient P (R) and the distributions of the Wigner reaction matrix [26] (in the literature often called K matrix [27]) for networks with time reversal symmetry (TRS) in the presence of moderate absorption strength γ = 2πΓ /∆ ≤ 7.7, where Γ is the absorption width and ∆ is the mean level spacing, have been investigated in [17,28]. Quite recently, the distribution of the reflection coefficient P (R) and the distributions of the Wigner reaction matrix for networks with TRS in the presence of much stronger absorption (γ > 19) have been studied experimentally and numerically in [25].…”