We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction ($K$) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random-matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering ($S$) and $K$ matrix of open quantum-chaotic systems and the two-point correlation function of the $S$-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph and attributed to the presence of nonuniversal short periodic orbits does not have any visible effects on the distributions of the reflection coefficients and the $K$ and $S$ matrices associated with the corresponding open quantum graph.

To synthesize lithium ferrite with various Gd concentrations (Li _0.5 Fe _2.5−x Gd _x O ₄ ), x = 0.00, 0.025, 0.05, 0.075, 0.1, solutes were dissolved in glycol, i.e. by using the without water and surfactant (WOWS) sol–gel method. X-ray diffraction (XRD) analysis confirmed that the material possessed an inverse spinel cubic structure and is single phase. Pellets of all samples were sintered at 700 °C and XRD confirmed that samples were crystalline, phase pure and had an inverse spinel cubic lattice. Scanning electron microscopy indicated that the grains were agglomerated and had a predominantly spherical shape. It is concluded that Gd acts as a grain refiner in lithium ferrite up to a Gd concentration of 0.05. AC conductivity and dielectric constant increased by increasing Gd concentration. The Maxwell–Wagner model and Johnsher’s power law were used to explain the dielectric properties. DC conductivity was measured from 100 to 600 °C. DC conductivity was explained by the hopping mechanism. It is concluded that DC resistivity and dielectric constant values are related reciprocally in the prepared sample. AC electrical properties were also measured at a constant frequency of 1 MHz in the temperature range from 400 to 600 °C. Gd-substituted lithium ferrite showed high AC conductivity, high DC resistivity and constant dielectric values, but low dielectric loss values as compared to pure lithium ferrite.

We present the experimental study of the distributions of the reflection amplitudes ri =|Sii| of the two-port scattering matrix S for networks with unitary and symplectic symmetries for the intermediate absorption strength parameter y. The experimental results confirm the theoretical predictions obtained within the framework of the Gaussian unitary and symplectic ensembles of the random matrix theory.