Proximity Effect and Multiple Andreev Reflections in Diffusive SNS   Junctions
  We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function. 
J.C. Cuevas, J. Hammer, J. Kopu, J.K. Viljas, and M. Eschrig