Multiple Andreev reflections as a transport problem in energy space

We present an approach for analyzing the dc current in voltage biased quantum superconducting junctions. We separate terms from different n-particle processes, i.e. single-particle, two-particle etc. 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 non-superconducting region described by an energy-dependent transfer matrix.