Non-equilibrium current noise in mesoscopic disordered SNS junctions

Current noise in superconductor-normal metal-superconductor (SNS) junctions is calculated within the scattering theory of multiple Andreev reflections (MAR). It is shown that the noise exhibits subharmonic gap singularities at $eV=2\Delta/n$, $n=1,2,... $ both in single-mode junctions with arbitrary transparency $D$ and in multi-mode disordered junctions. The subharmonic structure is superimposed with monotonic increase of the effective transferred charge $q^*=S_I(0)/2I$ with decreasing bias voltage. Other features of the noise include a step-like increase of $q^*$ in junctions with small $D$, and a divergence $S_I(0) \propto V^{-1/2}$ at small voltages and excess noise $S_{ex} = 2eI_{ex}$, where $I_{ex}$ is the excess current, at large voltages, in junctions with diffusive transport.