Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems

The Wigner-Smith time-delay of flux conserving systems is a real quantity that measures how long an excitation resides in an interaction region. The complex generalization of time-delay to non-Hermitian systems is still under development, in particular, its statistical properties in the short-wavelength limit of complex chaotic scattering systems has not been investigated. From the experimentally measured multi-port scattering (S)-matrices of one-dimensional graphs, a two-dimensional billiard, and a three-dimensional cavity, we calculate the complex Wigner-Smith (τWS), as well as each individual reflection (τₓₓ) and transmission (τxy) time-delays. The complex reflection time-delay differences (τδ R) between each port are calculated, and the transmission time-delay differences (τδ T) are introduced for systems exhibiting non-reciprocal scattering. Large time-delays are associated with coherent perfect absorption, reflectionless scattering, slow light, and uni-directional invisibility. We demonstrate that the large-delay tails of the distributions of the real and imaginary parts of each of these time-delay quantities are superuniversal, independent of experimental parameters: uniform attenuation η, number of scattering channels M, wave propagation dimension D, and Dyson symmetry class β. This superuniversality is in direct contrast with the well-established time-delay statistics of unitary scattering systems, where the tail of the τWS distribution depends explicitly on the values of M and β. Due to the direct analogy of the wave equations, the time-delay statistics described in this paper are applicable to any non-Hermitian wave-chaotic scattering system in the short-wavelength limit, such as quantum graphs, electromagnetic, optical and acoustic resonators, etc.