Pairing correlations in transport theories

A transport equation is derived for non-equilibrium systems with pairing correlations. The derivation is carried out in the closed-time-path (Schwinger-Keldysh) formalism using a generalization of the Gorkov equations for contour ordered Green functions. For an arbitrary non-equilibrium system two distribution functions are necessary for the description of the system obeying two coupled transport equations. In equilibrium, both distribution functions become equal. The limit of systems approaching equilibrium is discussed and a former derivation of an approximated transport equation for only one distribution function is justified. (orig.)