Phase-space approach to dynamical density functional theory

TL;DR

This paper derives a self-consistent, time-dependent equation for the one-body density of interacting particles with inertial Langevin dynamics, extending dynamical density functional theory to arbitrary dimensions.

Contribution

It introduces a novel derivation of dynamical density functional theory from kinetic theory, applicable in any dimension, using a systematic truncation and multiple time scale analysis.

Findings

Derived a new equation for the one-body density in inertial systems

Extended previous 1D work to arbitrary dimensions

Highlighted subtleties in kinetic theory derivation

Abstract

We consider a system of interacting particles subjected to Langevin inertial dynamics and derive the governing time-dependent equation for the one-body density. We show that, after suitable truncations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale analysis, we obtain a self-consistent equation involving only the one-body density. This study extends to arbitrary dimensions previous work on a one-dimensional fluid and highlights the subtelties of kinetic theory in the derivation of dynamical density functional theory.