Multiple Andreev reflections as a transport problem in energy space

We present an approach for analysing the dc current in voltage biased quantum superconducting junctions. By separating terms from different n -particle processes, we find that the n -particle current can be mapped on the problem of wave transport through a potential structure with n barriers. We discuss the relation between resonances in such structures and the subgap structures in the current–voltage characteristics. At zero temperature we find, exactly, that only processes creating real excitations contribute to the current. 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.