Abstract – In this letter we study the conductance G through one-dimensional quantum wires with disorder configurations characterized by long-tailed distributions (Lévy-type disorder). We calculate analytically the conductance distribution which reveals a universal statistics: the distribution of conductances is fully determined by the exponent α of the power-law decay of the disorder distribution and the average (lnG), i.e., all other details of the disorder configurations are irrelevant. For 0<α<1 we found that the fluctuations of lnG are not self-averaging and (lnG) scales with the length of the system as Lα, in contrast to the predictions of the standard scaling theory of localization where lnG is a self-averaging quantity and (lnG) scales linearly with L. Our theoretical results are verified by comparing with numerical simulations of one-dimensional disordered wires.
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