Gaussian factorization of hydrodynamic correlation functions and mode-coupling memory kernels

Abstract

A simple method to determine mode-coupling memory functions in generalized Langevin equations is obtained by explicitly expressing the random force of the slow hydrodynamic modes in terms of pair interactions in liquids and by Gaussian factoring the resulting multiple-point time correlation functions into products of linear correlation functions. The approach is used to derive the mode-coupling memory kernels for the velocity autocorrelation function, four-point bilinear density correlation function, and density correlation function of linear molecular liquids. These generalized Langevin equations and their associated memory kernels are useful for calculating relaxation processes and spectroscopic measurements in liquids and solvents. As a central result of our analysis, the non-Gaussian behavior of the bilinear density correlation function is quantitatively related to the nonexponential nature of linear hydrodynamic modes. This relation aids in the understanding of recent simulation results of non-Gaussian indicators in supercooled liquids.