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

The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics