Green's function approach to the non-equilibrium superconductivity near the critical line

In spite of the absent friction of super-currents, normal currents affect the superconducting condensate. The BCS approach with Bogoliubov-Valutin quasiparticles is not suited for description of the normal current near the critical line. We review an alternative theory of the non-equilibrium superconductivity dealing exclusively with normal-state quasiparticles. It is based on the Thouless T-matrix criterion, which is extended to non-equilibrium. The problem of selfconsistency of the T-matrix in the superconducting state is examined and solved with the help of the multiple-scattering theory. (paper)