Phase Fluctuations and Non-Equilibrium Josephson Effect

We consider a diffusive S-N-S junction with electrons in the normal layer driven out of equilibrium by external bias. We show that, the non-equilibrium fluctuations of the electron density in the normal layer cause the fluctuations of the phase of the order parameter in the S-layers. As a result, the magnitude of the Josephson current in the non-equilibrium junction is significantly supressed relative to its mean field value.