Velocity autocorrelation function of a Brownian particle

TL;DR

This study uses molecular dynamics simulations to analyze the velocity autocorrelation function of a Brownian particle, comparing results with theoretical models and highlighting the influence of solvent viscoelasticity.

Contribution

It provides a detailed comparison between simulation results and theoretical predictions for VACF, emphasizing the role of solvent viscoelasticity in decay behavior.

Findings

Long-time VACF matches hydrodynamic predictions.

Intermediate decay influenced by solvent viscoelasticity.

Simulation results align with analytic models at specific regimes.

Abstract

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [6] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point.We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.