Scaling theory of phase-coherent metallic conductors

We present a scaling theory for describing the smooth crossover from ballistic to diffusive transport in phase-coherent metallic conductors. The theory confirms a recent conjecture by Beenakker [Rev. Mod. Phys. $69,$ 731 (1997)], and represents a substantial improvement in the two-terminal version of Nazarov's circuit theory [Phys. Rev. Lett. $73,$ 134 (1994); $73,$ 1420 (1994)]. In addition, our approach allows for the explicit inclusion of interfaces of arbitrary transparency, which are described using the supersymmetric nonlinear σ model. The problem of two identical barriers separated by a diffusive conductor is solved exactly, and expressions for both the normal and Andreev conductances are presented.