Scattering theory for stationary materials with $\mathcal{PT}$ symmetry

A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in scattering from deterministic $\mathcal{PT}$-symmetric media, its stationary generalization involves two mechanisms leading to symmetry breaking in the statistics of scattered radiation, one stemming from the complex-valued medium realizations and the other - from the complex-valued degree of medium's correlation.