Influence of dissipation on phase tunneling in Josephson-junctions

The coupling between the phase and the electromagnetic field in the case of a tunnel junction is treated by Feynmans path integral method. It is shown that the elimination of the field leads to a frequency dependent mass for the motion of the phase ψ, which is simply related to the effective dielectric constant of the junction. Considering tunneling as a motion in imaginary time one obtains a polaron like mass enhancement connected to the dielectric function at positive imaginary frequencies, which essentially leads to the Caldeira-Leggett reduction of the elastic tunneling probability. In the weak damping limit it is shown that the emission of real excitations during tunneling is a higher order effect. At low temperatures the damping finally is determined by the linewidth of electromagnetic radiation at the Josephson plasma frequency.