Stochastic dynamics of collective modes for Brownian dipoles

TL;DR

This paper derives a Langevin equation for the microscopic local density of Brownian dipoles, incorporating both translational and rotational dynamics, enabling advanced theoretical approaches to colloidal systems.

Contribution

It introduces a Langevin equation for the local density of colloids with rotational degrees of freedom, bridging microscopic dynamics and continuum theories.

Findings

Derivation of a Langevin equation for local density including rotations

Framework for applying density functional theory to dipolar colloids

Potential for mode-coupling and other dynamical approximations

Abstract

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the starting point of a variety of approaches, ranging from dynamical density functional theory to mode-coupling approximations.