Dynamic Density Functional Theory of Fluids

TL;DR

This paper introduces a new time-dependent density functional theory for fluids that models their relaxational dynamics, validated against Langevin simulations, and discusses the role of thermal fluctuations and approximations.

Contribution

It develops a self-consistent deterministic equation for density evolution based on Langevin dynamics, incorporating an approximation for the correlation function, and compares it with existing stochastic methods.

Findings

Remarkable agreement with Langevin dynamics for 1D hard-rod system

Identifies limitations and interesting exceptions in the approach

Highlights the importance of the free energy functional form

Abstract

We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of the particles we are able by means of an approximated closure to derive a self-consistent deterministic equation for the temporal evolution of the average particle density. The closure is equivalent to assuming that the equal-time two-point correlation function out of equilibrium has the same properties as its equilibrium version. The changes in time of the density depend on the functional derivatives of the grand canonical free energy functional $F[\rho]$ of the system. In particular the static solutions of the equation for the density correspond to the exact equilibrium profiles provided one is able to determine the exact form of $F[\rho]$. In order to assess the validity of our approach we performed a comparison between the Langevin dynamics and the dynamic density functional method for a one-dimensional hard-rod system in three relevant cases and found remarkable agreement, with some interesting exceptions, which are discussed and explained. In addition, we consider the case where one is forced to use an approximate form of $F[\rho]$. Finally we compare the present method with the stochastic equation for the density proposed by other authors [Kawasaki,Kirkpatrick etc.] and discuss the role of the thermal fluctuations.