Topological properties of superconducting junctions

Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of $s$-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the $s$-matrix is always topologically trivial. We resolve an apparent contradiction with the previous results by taking into account the low-energy resonant poles of $s$-matrix. Thus no common topological transition occur in a finite junction. We reveal a transition of a different kind that concerns the configuration of the resonant poles.