Stochastic dynamics of collective modes for Brownian dipoles

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.

Figure 1

The left diagram has two $R$ internal lines, while the right one has an $R$ and a $C$ internal line (an arrowed leg denotes a response field $\overline{\psi }$ and a plain leg denotes the density field $\psi$).