Nonequilibrium Josephson effect in mesoscopic ballistic multiterminal SNS junctions

We present a detailed study of the nonequilibrium Josephson effect in quantum three- and four-terminal SNS devices. We focus our discussion on the anomalous de Josephson current which is a prominent feature of open nonequilibrium quantum SNS structures. This current is revealed under tunnel injection and it grows with the applied voltage across the injection point, in sharp contrast to the effect of nonequilibrium population of the Andreev states which induces oscillations and sign reversal of the Josephson current as a function of injection voltage. The anomalous current does not decay with the length of the junction even in the long junction limit L much greater than xi(T). This long-range effect is microscopically connected to the similar property of the injection current. We study the resonant features in the dependence of the Josephson current and the injection current on the injection voltage and superconducting phase difference, discuss the effect of asymmetry (a crossover to a-periodic phase dependence) and the role of resistive NS interfaces which introduce additional, normal electron, resonances. The Josephson effect is qualitatively similar in three- and four-terminal junctions, while the injection current in four-terminal junctions exhibits a specific resonant behavior due to Fano resonances.