Random scattering matrices and the circuit theory of Andreev conductances

The conductance of a normal-metal mesoscopic system in proximity to super-conducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a ''circuit'' with ''leads'' and ''junctions''. The junctions are each ascribed a scattering matrix which is averaged over the circular orthogonal ensemble, using recently developed techniques. The results for the electrical conductance reproduce and extend Nazarov's circuit theory, thus bridging between the scattering and the bulk approaches. The method is also applied to the heat conductance.