Transport in one-dimensional random resistor-superconductor mixtures with random distribution of resistor strength

The authors study the problem of transport in linear random resistor-superconductor mixtures with a random distribution of resistor strength. The superconductors with a concentration p are represented in the model as short circuits. The resistor concentration is (1-p) and their conductivity distribution is p( sigma ) approximately sigma ^{- alpha}, alpha <1. They find that for alpha >0 the specific conductivity scales with the linear size L of the system as L^{- alpha}(1- alpha )/(1-p)^-1(1- alpha )/. The mean square displacement (x²) of a random walker in this system scales as (x²) ^{(2- alpha )}(1- alpha/2 ) approximately (1-p) ^{-(2- alpha )}(1- alpha )/t. In the presence of a bias field they obtain (x)¹(1- alpha )/ approximately (1-p)^-1(1- alpha )/t. They present an exact enumeration method to study diffusion on those systems. The numerical results confirm the above scaling relations.