Overdamped van Hove function of atomic liquids

TL;DR

This paper derives a memory function equation for atomic liquids' density fluctuations and demonstrates a long-time dynamic equivalence with Brownian liquids through simulations.

Contribution

It introduces a generalized Langevin equation approach to connect atomic and Brownian liquid dynamics, revealing a fundamental equivalence.

Findings

Long-time dynamics of atomic and Brownian liquids are equivalent.

Simulation results confirm the theoretical dynamic equivalence.

The derived memory function formalism captures key fluctuation behaviors.

Abstract

Using the generalized Langevin equation formalism and the process of contraction of the description we derive a general memory function equation for the thermal fluctuations of the local density of a simple atomic liquid. From the analysis of the long-time limit of this equation, a striking equivalence is suggested between the long-time dynamics of the atomic liquid and the dynamics of the corresponding \emph{Brownian} liquid. This dynamic equivalence is confirmed here by comparing molecular and Brownian dynamics simulations of the self-intermediate scattering function and the long-time self-diffusion coefficient for the hard-sphere liquid.