Abstract
The existence of mesoscopic conductance fluctuations invalidates the traditional concept of impurity average conductances even for metallic systems which are much larger than the inelastic-scattering length. We use the methodology of classical conductance networks in order to incorporate the effect of mesoscopic conductance fluctuations in a self-consistent extended scheme for computing macroscopic conductances. Scaling ideas are reconsidered with a main emphasis on the two-dimensional disordered electron gas and, in particular, the integral quantum Hall regime. We find that the singularity structures of the theories of ``macroscopic'' and ``impurity averaged'' conductances are quite generally the same. Significant numerical differences may occur, however, in the regime of strong quantum interference effects. Specific experimental work on the integral quantum Hall regime is being proposed for the purpose of resolving some of the outstanding questions raised in this paper.
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