Multiple Andreev reflections as a transport problem in energy space

We present an approach for analysing the de current in voltage biased quant um superconducting junctions. By separating terms from different n-particle processes, we find that the n-particle current can be mapped on the proble m of wave transport through a potential structure with n barriers. We discu ss the relation between resonances in such structures and the subgap struct ures in the current-voltage characteristics. At zero temperature we find, e xactly, that only processes creating real excitations contribute to the cur rent. Our results are valid for a general SXS junction, where the X region is an arbitrary nonsuperconducting region described by an energy-dependent transfer matrix. (C) 1999 Academic Press.