Scaling theory of phase-coherent metallic conductors -: art. no. 033306

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 sigma 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.