Statistics of Complex Wigner Time Delays as a counter of Smatrix poles: Theory and Experiment
Abstract
We study the statistical properties of the complex generalization of Wigner time delay $\tau_\text{W}$ for subunitary wave chaotic scattering systems. We first demonstrate theoretically that the mean value of the $\text{Re}[\tau_\text{W}]$ 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 timereversal 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 shortwavelength limit.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.15469
 Bibcode:
 2021arXiv210615469C
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 8 pages, 3 figures. Supplementary material added