In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffusion. For mesoscopic junctions with small capacitance the phase undergoes large quantum fluctuations, and the current is also decreased by Coulomb blockade effects. We discuss the behavior of the current-voltage characteristics in a large range of parameters comprising the phase diffusion regime with coherent Josephson current as well as the supercurrent peak due to incoherent Cooper pair tunneling in the Coulomb blockade regime.
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