Abstract
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 closedform in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephsoncurrent in the classical regime as well as the supercurrent peakdue to incoherent Cooper pair tunneling in the Coulomb blockade regime.
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