# Self-consistent generalized Langevin equation theory of the dynamics of multicomponent atomic liquids

## TL;DR

This paper develops a self-consistent generalized Langevin equation theory to describe the long-time dynamics of multicomponent atomic liquids, bridging the gap between colloidal and atomic liquid behaviors.

## Contribution

It introduces a new approximate but quantitative theoretical framework for atomic liquids based on a dynamic equivalence with colloids, validated by molecular dynamics simulations.

## Key findings

- The theory accurately predicts long-time diffusive behavior.
- It captures the transition from ballistic to diffusive motion.
- Simulations confirm the theory's qualitative and quantitative predictions.

## Abstract

A fundamental challenge of the theory of liquids is to understand the similarities and differences in the macroscopic dynamics of both colloidal and atomic liquids, which originate in the (Newtonian or Brownian) nature of the microscopic motion of their constituents. Starting from the recently-discovered long-time dynamic equivalence between a colloidal and an atomic liquid that share the same interparticle pair potential, in this work we develop a self-consistent generalized Langevin equation (SCGLE) theory for the dynamics of equilibrium multicomponent atomic liquids, applicable as an approximate but quantitative theory describing the long-time diffusive dynamical properties of simple equilibrium atomic liquids. When complemented with a Gaussian-like approximation, this theory is also able to provide a reasonable representation of the passage from ballistic to diffusive behavior. We illustrate the applicability of the resulting theory with three particular examples, namely, a monodisperse and a polydisperse monocomponent hard-sphere liquid, and a highly size-asymmetric binary hard-sphere mixture. To assess the quantitative accuracy of our results, we perform event-driven molecular dynamics simulations, which corroborate the general features of the theoretical predictions.