  We describe a test particle approach based on dynamical density functional
theory (DDFT) for studying the correlated time evolution of the particles that
constitute a fluid. Our theory provides a means of calculating the van Hove
distribution function by treating its self and distinct parts as the two
components of a binary fluid mixture, with the `self' component having only one
particle, the `distinct' component consisting of all the other particles, and
using DDFT to calculate the time evolution of the density profiles for the two
components. We apply this approach to a bulk fluid of Brownian hard spheres and
compare to results for the van Hove function and the intermediate scattering
function from Brownian dynamics computer simulations. We find good agreement at
low and intermediate densities using the very simple Ramakrishnan-Yussouff
[Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy
functional. Since the DDFT is based on the equilibrium Helmholtz free energy
functional, we can probe a free energy landscape that underlies the dynamics.
Within the mean-field approximation we find that as the particle density
increases, this landscape develops a minimum, while an exact treatment of a
model confined situation shows that for an ergodic fluid this landscape should
be monotonic. We discuss possible implications for slow, glassy and arrested
dynamics at high densities.
