  The supercurrent of a Josephson junction is reduced by phase diffusion. For
ultrasmall capacitance junctions the current may be further decreased by
Coulomb blockade effects. We calculate the Cooper pair current by means of
time-dependent perturbation theory to all orders in the Josephson coupling
energy and obtain the current-voltage characteristic in closed form in a range
of parameters of experimental interest. The results comprehend phase diffusion
of the coherent Josephson current in the classical regime as well as the
supercurrent peak due to incoherent Cooper pair tunneling in the strong Coulomb
blockade regime.
