Two-time and two-frequency correlators

In this system with simple statistics (thermal mixtures) and analytical solutions, it is very interesting to investigate different kinds of correlators as a reference for other systems and in order to understand their physical meaning. Some quantities that I am analyzing at present are the two-frequency correlator, $S^{(2)}(\omega_1,\omega_2)$ , and the frequency resolved two-photon counting correlator, $S^{(2)}(t_1,\omega_1;t_2,\omega_2)$ , given by the integral (2.110). A first approximation to the problem can be made with Eq. (3.13).