Nonequilibrium Josephson current in ballistic multiterminal SNS-junctions

We study the nonequilibrium Josephson current in a long two-dimensional ballistic SNS-junction with a normal reservoir coupled to the normal part of the junction. The current for a given superconducting phase difference $\phi$ oscillates as a function of voltage applied between the normal reservoir and the SNS-junction. The period of the oscillations is $\pi \hbar v_F/L$, with $L$ the length of the junction, and the amplitude of the oscillations decays as $V^{-3/2}$ for $eV \gg \hbar v_{F}/L$ and zero temperature. The critical current $I_c$ shows a similar oscillating, decaying behavior as a function of voltage, changing sign every oscillation. Normal specular or diffusive scattering at the NS-interfaces does not qualitatively change the picture.