Velocity autocorrelation function for simple liquids and its application to liquid metals and alloys

The single-particle Brownian motion in simple monatomic liquids has been described with the help of the equation of motion in terms of velocity autocorrelation function psi(t) , where the particle is assumed to diffuse in a mean-time-dependent field. The equation of motion which is a second order differential equation in psi(t) has been solved in terms of nth order Bessel functions of the first and second kind. The solution is, in fact, the generalization of the solution given by Glass and Rice (GR) [Phys. Rev. 176, 239 (1968)] for low density fluids. The generalized solution is an improvisation over the one by GR and the results demonstrate that, for high density liquids such as liquid metals where the GR solution fails to give a reasonable account of psi(t) , the generalized solution could be very useful to calculate psi(t) . The present approach has been applied to the liquid alkali metals and binary alloys. The results are found to be in close agreement with the molecular dynamics results.