Nonadiabatic analysis of the Josephson critical current influenced by quantum phase fluctuations

The influence of the electromagnetic environment on the dc Josephson current is studied allowing for nonadiabatic motion of the phase difference across a junction. The critical current is evaluated nonperturbatively within mean-field theory, fully taking into account the nonlocal kernels in the Ambegaokar-Eckern-Schoen effective action. It turns out that the adiabatic approximation, which can be justified when the superconducting energy gap exceeds the charging energy, yields qualitatively correct results even for the opposite case, although quantitative deviations from the adiabatic approximation are found to be substantial in some experimentally accessible regions