Conductance through quantum wires with Levy-type disorder: universal statistics in anomalous quantum transport

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