Memory Function of Velocity Autocorrelation of Classical Liquids

To take into account the collective aspects of motion of liquid atoms, an expression for the memory function of a classical liquid has been formulated from the equations for the velocity autocorrelation function by using the approaches of Kerr and Singwi et al. for atomic motion in classical liquids. This expression satisfies the moment relation, and its long-time behavior shows a $t^{-\frac{3}{2}}$ dependence. Furthermore, approximate calculations for the memory function in liquid argon are made by using our expression and incorporating the contribution due to the hard-core part of the potential from the expression of Singwi et al. These calculations show the presence of a minimum in the memory function near 4 × ${10}^{-13\mathrm{}}$ sec.