  The dynamics of individual colloidal particles in random potential energy
landscapes were investigated experimentally and by Monte Carlo simulations. The
value of the potential at each point in the two-dimensional energy landscape
follows a Gaussian distribution. The width of the distribution, and hence the
degree of roughness of the energy landscape, was varied and its effect on the
particle dynamics studied. This situation represents an example of Brownian
dynamics in the presence of disorder. In the experiments, the energy landscapes
were generated optically using a holographic set-up with a spatial light
modulator, and the particle trajectories were followed by video microscopy. The
dynamics are characterized using, e.g., the time-dependent diffusion
coefficient, the mean squared displacement, the van Hove function and the
non-Gaussian parameter. In both, experiments and simulations, the dynamics are
initially diffusive, show an extended sub-diffusive regime at intermediate
times before diffusive motion is recovered at very long times. The dependence
of the long-time diffusion coefficient on the width of the Gaussian
distribution agrees with theoretical predictions. Compared to the dynamics in a
one-dimensional potential energy landscape, the localization at intermediate
times is weaker and the diffusive regime at long times reached earlier, which
is due to the possibility to avoid local maxima in two-dimensional energy
landscapes.
