SCALING THEORY OF CONDUCTION THROUGH A NORMAL-SUPERCONDUCTOR MICROBRIDGE

The length dependence of the resistance of a disordered normal-metal wire attached to a superconductor is computed. The scaling of the transmission eigenvalue distribution with length is obtained exactly in the metallic limit by a transformation onto the isobaric flow of a two-dimensional ideal fluid. The resistance has a minimum for lengths near l/GAMMA, with l the mean free path and GAMMA the transmittance of the superconductor interface.