The symbolically denoted ⋯ ⋯ | s c a t t e r contributions stem from the hierarchical coupling due to many-body interactions. Conceptually, P k , f k e , and f k h are single-particle expectation values while the hierarchical coupling originates from two-particle correlations such as polarization-density correlations or polarization-phonon correlations. Physically, these two-particle correlations introduce several nontrivial effects such as screening of Coulomb interaction, Boltzmann-type scattering of f k e and f k h toward Fermi–Dirac distribution, excitation-induced dephasing, and further renormalization of energies due to correlations.