Two-Phonon Response of Anharmonic Lattices in the First-Order Self-Consistent Phonon Approximation

Further extensions are made to a previously developed analysis for the two-time correlation functions in anharmonic lattices within the first-order self-consistent phonon approximation. This stationary-variation approximation is shown to represent an energy minimum if and only if the one-phonon response is stable. An explicit expression is exhibited for the two-phonon response and is interpreted as yielding an effective interaction between phonons. It is shown that the first-order approximation is not fully adequate for describing transport properties (e. g., thermal conductivity) or for investigating resonances or bound states of the two phonons. The distortion of the one-phonon peak in the inelastic-neutron or Raman-scattering cross section due to the finite size of the momentum transfer is investigated in more detail than the previous analysis.