On the relative dynamics of pairs of atoms in simple liquids

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 r0 in a given distance range a0⩽r0⩽b0 at time 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 genealized Langevin equation is obtained which is solved numericall. Time dependent cross correlations from the MD-data. The resulting memory functions surprisingly prove to be practically independent of the chosen interval (a0b0) 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 it is 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.