SUPPRESSION OF THE JOSEPHSON CURRENT BY QUANTUM PHASE FLUCTUATIONS - BEYOND THE ADIABATIC APPROXIMATION

We study how the Josephson current in a shunted junction is suppressed when the energy gap DELTA is not large compared to the charging energ y E(C). Then the time dependence of the nonlocal kernels in the effect ive action describing the junction becomes important. For low ratios o f the Josephson energy to E(C), the Josephson current deviates by tens of percent from what one obtains in the adiabatic limit (i.e. DELTA > > E(C)).