Universal and nonuniversal properties of wave-chaotic scattering systems

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.

Figure 1

(Color online) Plot of the impedance from the average of 100 cavity realizations $⟨Z⟩$ versus frequency from 6 to 8 GHz with perturbers inside the cavity. Shown are the real (three upper curves) and the imaginary parts (three lower curves) of the impedance for the theory ($Z_{avg}^{\left(L\right)}$ with $L=200\text{cm}$, blue dashed) and the experiment ($⟨Z⟩$, red solid), as well as the measured radiation impedance of the port ($Z_R$, black thick). Inset: The wave-chaotic two-dimensional cavity with perturbers and a single port.

Figure 2

(Color online) The average ${\chi }^2$ of distributions of the phase of the scattering parameter ${\phi }_s$ on a semilogarithmic scale, where the scattering parameters are calculated from impedance normalized with only the radiation impedance (green) and with ray trajectories according to the maximum trajectory length from $L=50\text{cm}$ (red) up to $L=200\text{cm}$ (blue) versus frequency window sizes from 0.1 to 4.0 GHz.

Figure 3

(Color online) Plot of the smoothed impedance versus frequency from 6 to 8 GHz. Shown are the real (three upper curves) and the imaginary part (three lower curves) of the smoothed impedance for the theory ($Z^{\left(L\right)}$ with $L=200\text{cm}$, blue dashed) and the experiment (red solid), as well as the measured radiation impedance of the port ($Z_R$, black thick).