Abstract
We discuss the effect of fluctuations of the random potential in directions transverse to the current flow in a modified Migdal-Kadanoff approach to probabilistic scaling of conductance with size L, in d-dimensional metallic systems. The conductance cumulants are finite and vary as L d−1− n for n ⩾ 2 i.e. conductance fluctuations are constant for d = 3. The mean conductance has a non-classical correction with dln g ̄ /dln L = d − 2 − (3 g ̄ ) −1 for d ⩾ 2. The form of the higher cumulants is strongly influenced by the transverse potential fluctuations and may be compared with the results of perturbative diagrammatic approaches.
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