A theoretical extension for the electrical conductivity of molten salts

A microscopic description for the partial DC conductivities in molten salts developed by the present authors is briefly summarised, starting from the Langevin equation for the constituent ions. It is clarified that the memory function gamma(t) should be written as the form of gamma(t) = (gamma) over bar (2)(0)f(t), in which (gamma) over bar is the Fourier-Laplace transform in the long wavelength limit and the integration from zero to infinity for f(t) being unity. To solve the mutual relation between the combined velocity correlation functions to elucidate the DC conductivities Z(sigma)(+/-)(t) and the memory function gamma(t) of the Langevin equation in a short time region, we propose a new recursion method. Practical application is carried out for the derivation of the fitted memory function from the Z(sigma)(+/-)(t) of molten NaCl obtained by MD simulation. This fitted function in the short time region is approximated to a summation of three kinds of the Gaussian functions, and their physical interpretations are discussed.