The approach to equilibrium in a pure superconductor the relaxation of the Cooper pair density

Electron-phonon and electron-electron collisions are the processes which determine the relaxation timeτ _R of the Cooper pair density. The case is considered for which the deviation of the pair density from equilibrium is small and where the equilibrium state is homogeneous. Starting from the Eliashberg equation, one is able to reduce the problem to a quadrature once the equilibrium Green functions are known. If the deviation is constant in space, andT/T _c?0.5, we find (tau _R approx sqrt {T_c /(T_c - T)} tau _c) , whereτ _c is the collision time (≈10^?8 sec). For a deviation modulated in space,τ _R very quickly reaches the limiting valueτ _c.