Theory of the cos phi term in the Josephson tunneling current

The current--phase relation for the Josephson tunnel junction is investigated by using the time-dependent Ginzburg--Landau (TDGL) equations. The cos phi term is shown to have a negative coefficient and the same order of magnitude as the phase-independent term. The effect of the tunneling barrier is taken into account in terms of the boundary conditions of the order parameter and the electric potential at the junction; the new boundary conditions are derived by generalizing de Gennes' discussions for the dc Josephson effect to the time-dependent phenomena. The TDGL equations are solved on the assumption that the transmission coefficient across the junction is small enough and that the processes involved are quasi-stationary. It is concluded that the spatial and temporal variations of various quantities are of vital importance to an understanding of the nonequilibrium characteristics in the tunnel junction