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 $\varphi$ oscillates as a function of voltage applied between the normal reservoir and the SNS-junction. The period of the oscillations is $\pi \mathrm{\hslash }{v}_F\mathrm{/}L$, with $L$ the length of the junction, and the amplitude of the oscillations decays as $V^{-3\mathrm{/}2}$ for $eV\gg \mathrm{\hslash }{v}_F\mathrm{/}L$ 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.