Dynamics of atomic pairs in a Lennard-Jones fluid: Mean relative displacement analysis

We have analyzed the dynamics of atomic pairs in a simple fluid in terms of the mean relative displacement of two atoms with a given initial separation. The short-time expansion of the mean relative displacement has been derived exactly beyond the constant acceleration approximation (CAA) (up to the t⁴ order). For a Lennard-Jones fluid, the mean relative displacements calculated by either the CAA or the t⁴-order approximation have been compared with the results obtained from a molecular-dynamics simulation. Through studying the relative motions of atomic pairs with different initial separations, we give a physical picture of the dynamics of neighboring atoms beyond the CAA.