Statistics of Complex Wigner Time Delays as a Counter of S-Matrix Poles: Theory and Experiment

We study the statistical properties of the complex generalization of Wigner time delay tau(W) for subunitary wave-chaotic scattering systems. We first demonstrate theoretically that the mean value of the Re[tau(W)] distribution function for a system with uniform absorption strength eta is equal to the fraction of scattering matrix poles with imaginary parts exceeding eta. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave-chaotic scattering system in the short-wavelength limit, including quantum wires and dots, acoustic and electromagnetic resonators, and quantum graphs.

Automated summary

Through experimental and theoretical analysis, we studied the statistical properties of complex Wigner time delay in subunitary wave-chaotic scattering systems. Experimental results showed good agreement with the developed theory.