# A simple closure procedure for the study of velocity autocorrelation functions in fluids as a "bridge" between different theoretical approaches

## TL;DR

This paper introduces a simple closure procedure for analyzing velocity autocorrelation functions in fluids, effectively bridging different theoretical models and improving agreement with molecular dynamics data across various densities.

## Contribution

A novel closure method based on summing continued fractions that enhances the accuracy of VAF predictions and connects various theoretical approaches.

## Key findings

- Method yields better agreement with MD data than Markovian approximation.
- Density dependence of transition time to hydrodynamic behavior is quantified.
- Method relates to GCM and MCT theories, providing a unified framework.

## Abstract

Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the MD data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode (GCM) theory, the mode coupling theory (MCT), and some other theoretical approaches.