Scattering theory for stationary materials with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry

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