Two-particle correlation functions in superconductors below the transition temperature

Order parameter fluctuations are calculated at temperatures below the critical temperature by treating pairing vibrations, density fluctuations, and coupling between them within a matrix framework. The calculations have been performed for both neutral and charged superconductors in the presence of normal impurities and pair-breaking agencies with specialization to the dirty limit. The correlation functions, evaluated for frequencies small compared to the temperature, break up into fluctuations of phase and amplitude of the order parameter. An expression for the longitudinal dielectric function is given. The two branches of gapless and gap behavior are discussed. Comparison with the diffusive time-dependent Ginzburg-Landau equations makes it possible to estimate the range of validity of the latter.