On the relative dynamics of pairs of atoms in simple liquids (Q1080294)

We have studied the mutual dynamics of pairs of atoms in a dense Lennard- Jones fluid by evaluating relative velocity autocorrelation functions for particle pairs with separation \(r_ 0\) in a given distance range \(a_ 0\leq r_ 0\leq b_ 0\) at time zero using computer simulation. By application of projection operator techniques we have further derived exact generalized Langevin and Fokker-Planck equations for the problem in hand. After introducing simplifying assumptions for the memory kernel of these equations, a generalized Langevin equation is obtained which is solved numerically. Time dependent cross correlations between the relative velocity and the mean force entering this calculation are also evaluated from the MD-data. The resulting memory functions surprisingly prove to be practically independent of the chosen interval \((a_ 0,b_ 0)\) of starting separations of pair trajectories and, consequently, on the sign of the mean force between the test particles at time equal zero. The memory function exhibits a short time initial decay and a weak positive long time tail. Neglecting the latter and approximating the short time regime by a separation independent exponential memory function is it possible to model the pair dynamics by stochastic dynamics techniques. The mutual velocity correlation functions, force-velocity cross correlation functions and relative positional moments obtained from a stochastic dynamics simulation agree semi-quantitatively with the corresponding ''exact'' correlation functions obtained from MD-simulations.