Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory

TL;DR

This paper develops an order-preserving dynamical density functional theory (DDFT) for one-dimensional systems, accurately capturing long-time caging effects, single-file diffusion, and boundary behaviors in confined colloids.

Contribution

It introduces a novel DDFT approximation that maintains particle order, enabling precise modeling of long-time dynamics and caging effects in one-dimensional colloidal systems.

Findings

Accurately reproduces boundary behaviors of confined hard rods.

Captures long-time subdiffusive behavior characteristic of single-file diffusion.

Provides exact results at system boundaries and correct long-time density profiles.

Abstract

Dynamical density functional theory (DDFT) is a powerful variational framework to study the nonequilibrium properties of colloids by only considering a time-dependent one-body number density. Despite the large number of recent successes, properly modeling the long-time dynamics in interacting systems within DDFT remains a notoriously difficult problem, since structural information, accounting for temporary or permanent particle cages, gets lost. Here we address such a caging scenario by reducing it to a clean one-dimensional problem, where the particles are naturally ordered (arranged on a line) by perfect cages created by their two next neighbors. In particular, we construct a DDFT approximation based on an equilibrium system with an asymmetric pair potential, such that the corresponding one-body densities still carry the footprint of particle order. Applied to a system of confined hard rods, this order-preserving dynamics (OPD) yields exact results at the system boundaries, in addition to the imprinted correct long-time behavior of density profiles representing individual particles. In an open system, our approach correctly reproduces the reduced long-time diffusion coefficient and subdiffusion, characteristic for a single-file setup. These observations cannot be made using current forms of DDFT without particle order.