The Random Coupling Model (RCM) predicts the statistical properties of waves inside a ray-chaotic enclosure in the semiclassical regime by using Random Matrix Theory, combined with system-specific information. Experiments on single cavities are in general agreement with the predictions of the RCM. It is now desired to test the RCM on more complex structures, such as a cascade or network of coupled cavities, that represent realistic situations but that are difficult to test due to the large size of the structures of interest. This paper presents an experimental setup that replaces a cubic-meter-scale microwave cavity with a miniaturized cavity, scaled down by a factor of 20 in each dimension, operated at a frequency scaled up by a factor of 20 and having wall conductivity appropriately scaled up by a factor of 20. We demonstrate experimentally that the miniaturized cavity maintains the statistical wave properties of the larger cavity. This scaled setup opens the opportunity to study wave properties in large structures such as the floor of an office building, a ship, or an aircraft, in a controlled laboratory setting.

The statistics of scattering of waves inside single ray-chaotic enclosures have been successfully described by the Random Coupling Model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with variable coupling scenarios. The statistical properties of the model-generated quantities are tested against measured data of electrically large multi-cavity systems of various designs. The statistics of model-generated trans-impedance and induced voltages on a load impedance agree well with the experimental results. The RCM coupled chaotic enclosure model is general and can be applied to other physical systems including coupled quantum dots, disordered nanowires, and short-wavelength electromagnetic propagation through rooms in buildings, aircraft and ships. arXiv:1909.03827v1 [physics.class-ph]

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Random matrix theory successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model oers a complete statistical model with a simple additive formula in terms of impedance to combine the predictions of random matrix theory and nonuniversal system-specic features. The statistics of measured wave properties generally have nonuniversal features. However, ratios of the variances of elements of the impedance matrix are predicted to be independent of such nonuniversal features and thus should be universal functions of the overall system loss. In contrast with impedance variance ratios, scattering variance ratios depend on nonuniversal features unless the system is in the high loss regime. In this paper, we present numerical tests of the predicted universal impedance variance ratios and show that an insucient sample size can lead to apparent deviation from the theory, particularly in the low loss regime. Experimental tests are carried out in three two-port microwave cavities with varied loss parameters, including a novel experimental system with a superconducting microwave billiard, to test the variance-ratio predictions in the low loss time-reversal-invariant regime. It is found that the experimental results agree with the theoretical predictions to the extent permitted by the nite sample size.

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