Mesoscopic Josephson effect

In the classical Josephson effect the phase difference across the junction is well defined, and the supercurrent is reduced only weakly by phase diffu sion. For mesoscopic junctions with small capacitance the phase undergoes l arge quantum fluctuations, and the current is also decreased by Coulomb blo ckade effects. We discuss the behavior of the current-voltage characteristi cs in a large range of parameters comprising the phase diffusion regime wit h coherent Josephson current as well as the supercurrent peak due to incohe rent Cooper pair tunneling in the Coulomb blockade regime. (C) 1999 Academi c Press.