On the relative dynamics of pairs of atoms in simple liquids

Abstract

Abstract 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 ⩽ r 0 ⩽ b 0 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 ( 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 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.