A Green´s function approach to the dynamics-controlled truncation formalism: Derivation of the /spl chi//sup (3)/ equations of motion

Summary form only given. The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that gives a complete description of all coherent phenomena in optically excited semiconductors to certain low orders (e.g., /spl chi//sup (3)/) in the external field. Its most important application to date has been the elucidation of exciton-exciton correlation effects in four-wave-mixing experiments in the /spl chi//sup (3)/ regime. We have examined in detail the standard Feynman-Dyson perturbation theory diagrams for the (Keldysh path-ordered) Green´s functions corresponding to the interband polarization, the one-particle density matrix, and the coherent biexcitonic (four-point) correlation function. The Coulomb matrix elements for transitions between conduction and valence bands are excluded, and the initial state is taken to be the electron-hole vacuum. The crucial result from this examination is that these two conditions annihilate a vast class of order.