Abstract
The scaling theory of Anderson localization is based on a global conductancegL that remains a random variable of order O(1) at criticality. One realization of such aconductance is the Landauer transmission for many transverse channels. On the otherhand, the statistics of the one-channel Landauer transmission between two local probes isdescribed by a multifractal spectrum that can be related to the singularity spectrum ofindividual eigenstates. To better understand the relations between these two types ofresults, we consider various scattering geometries that interpolate between these two casesand analyze the statistics of the corresponding transmissions. We present detailednumerical results for the power-law random banded matrices (PRBM model). Ourconclusions are: (i) in the presence of one isolated incoming wire and many outgoing wires,the transmission has the same multifractal statistics as the local density of statesof the site where the incoming wire arrives and (ii) in the presence of backwardscattering channels with respect to case (i), the statistics of the transmission isnot multifractal anymore, but becomes monofractal. Finally, we also describehow these scattering geometries influence the statistics of the transmission offcriticality.
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