Effect of environment fluctuations on a Josephson current

An influence of an electromagnetic environment on a Josephson current through a tunnel junction is studied with the aid of Ambegaokar-Eckern-Schön effective action. Two types of environment are investigated: one, characterized by a resonant mode, and an ohmic one. The crossover to a Josephson π-junction is possible for both of them. In addition the resonant-mode environment results in an increase of a Josephson current when the ratio of the doubled superconducting gap to the frequency of the mode is close to an integer number.