A scaling principle for the dynamics of density fluctuations in atomic liquids

On the basis of the fully renormalized kinetic theory of equilibrium classical atomic fluids, we conjecture that different fluids with very different interatomic potentials might have very similar dynamical density fluctuations if they have similar static pair correlation functions. This conjecture, which we call approximate scaling relationship, is the main focus of this work. We also present the results of molecular dynamics simulations which provide empirical support for this conjecture. The approximate scaling relationship suggests that in order to understand how the interatomic potential of a fluid determines its dynamical properties, it is worthwhile focussing separately on the two questions of how the potential affects the pair correlation function and how the pair correlation function affects the dynamics.; The molecular dynamics simulations were performed on two different atomic fluids. One fluid has the particles interacting via a Lennard-Jones potential and the other fluid has particles interacting via the repulsive part of the Lennard-Jones potential. Though these systems have significantly different potentials, we have found pairs of systems which we call corresponding states which have very similar static pair correlation functions. Each pair of corresponding states consists of a Lennard-Jones fluid at one temperature and a repulsive Lennard-Jones fluid at a lower temperature. The approximate scaling principle predicts that the time dependent correlation functions of the two systems in a pair of corresponding states should be very similar, provided that the times of the two systems are scaled appropriately.; We have investigated the behavior of a variety of dynamical correlation functions including the intermediate scattering function, the incoherent intermediate scattering function, the velocity autocorrelation function, the transverse current correlation function, the longitudinal current correlation function, and the self longitudinal current correlation function. We have found striking similarities in the behavior of the correlation functions of corresponding states especially for long times. Furthermore, the self diffusion coefficients and the shear viscosities for corresponding states are similar.; We discuss the implications of these results for the kinetic theory of fluids.