Using orthogonal polynomials, a novel approach for studying DC and AC
conductivity and velocity-velocity correlation function has been devel
oped. The method works in direct space and can treat order or disorder
ed, finite or infinite, and pure or alloy systems with equal ease. Fur
ther, it is not computer intensive and allows conductivity calculation
s as a function of frequency or the location of the Fermi energy in an
efficient manner.