Effect of zero point phase fluctuations on Josephson tunneling

In the presence of phase fluctuations the de Josephson effect is modified and the supercurrent at zero voltage is replaced by a peak at small but finite voltages, it is shown that at zero temperature this peak is determined by two complementary expansions of finite radius of convergence. The leading order expressions are related to results known from the regimes of Coulomb blockade and of macroscopic quantum tunneling. The peak positions and the suppression of the critical current by quantum fluctuations are discussed.