Green's function approach to the dynamics-controlled truncation formalism: derivation of the χ(3) equations of motion

A study was carried out to examine in detail the standard Feynman-Dyson perturbation theory diagrams for the Green's functions corresponding to the interband polarization, the one-particle density matrix, and the coherent biexcitonic correlation function. The surviving diagrams were classified in increasing order of the external field. In each order up to order three, it was shown that all non-vanishing terms contributing to the relevant Green's functions can be ressumed to yield closed equations of motion.