Dynamical density functional theory for dense atomic liquids

TL;DR

This paper develops a dynamical density functional theory for dense atomic liquids, linking equilibrium free energy functionals to dynamic density profiles and providing insights into sound speed and glass transition phenomena.

Contribution

It introduces a DDFT derived from Newton's equations that leverages equilibrium free energy functionals to accurately describe dense atomic liquid dynamics.

Findings

Correctly predicts the speed of sound in dense liquids

Can be used to derive mode coupling theory for glass transition

Provides a framework for inhomogeneous atomic fluid dynamics

Abstract

Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids.