Conductivity of a random electron chain renormalization group approach

We apply a recently proposed decimation procedure together with renormalization group techniques to the study of the conductivity of a one-dimensional random electron chain represented by Anderson's Hamiltonian. Decimation generates recursion relations for the random parameters that are converted into recursion integral equations for the probability distribution functions. For particular initial values of the random parameters the integral equations are solved exactly, showing the flow of the system to a localized state. The conductivity of a tight-binding model is calculated and its average over the probability distribution functions discussed previously shows the expected exponential decrease with the system size.