Chaotic scattering with localized losses: S-matrix zeros and reflection time difference for with broken time-reversal invariance

Motivated by recent studies of the phenomenon of coherent perfect absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as well as of the recently introduced reflection time difference (RTD). The latter plays the same role for S-matrix zeros as the Wigner time delay does for its poles. For systems with broken time-reversal invariance, we derive the n-point correlation functions of the zeros in a closed determinantal form, and we study various asymptotics and special cases of the associated kernel. The time-correlation function of the RTD is then evaluated and compared with numerical simulations. This allows us to identify a cubic tail in the distribution of RTD, which we conjecture to be a superuniversal characteristic valid for all symmetry classes. We also discuss two methods for possible extraction of S-matrix zeros from scattering data by harmonic inversion.