The dynamics of colloidal particles in potential energy landscapes have mainly been investigated theoretically. In contrast, here we discuss the experimental realization of potential energy landscapes with the help of light fields and the observation of the particle dynamics by video microscopy.The experimentally observed dynamics in periodic and random potentials are compared to simulation and theoretical results in terms of, e.g. the mean-squared displacement, the time-dependent diffusion coefficient or the non-Gaussian parameter. The dynamics are initially diffusive followed by intermediate subdiffusive behaviour which again becomes diffusive at long times. How pronounced and extended the different regimes are, depends on the specific conditions, in particular the shape of the potential as well as its roughness or amplitude but also the particle concentration. Here we focus on dilute systems, but the dynamics of interacting systems in external potentials, and thus the interplay between particle-particle and particle-potential interactions, is also mentioned briefly. Furthermore, the observed dynamics of dilute systems resemble the dynamics of concentrated systems close to their glass transition, with which it is compared. The effect of certain potential energy landscapes on the dynamics of individual particles appears similar to the effect of interparticle interactions in the absence of an external potential.

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 subdiffusive 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.

Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general.

From molecular dynamics simulations results are reported concerning correlations between low-frequency (lf) heterogeneous dynamics in simulated Ni0.5Zr0.5 melts at 700, 760, and 810 K, which means around the Kauzmann temperature of the model, TK approximately 750 K. A method is presented to separate lf dynamics, reflecting the slow relaxation dynamics in the vitrifying melt, and high-frequency (hf) dynamics, characteristic of the thermal fluctuations at the considered temperatures. By means of a suitable quantitative measure of the distribution of heterogeneous lf dynamics in space and time, correlation parameters are evaluated between the spatial distribution of lf dynamics and structural inhomogeneities in the thermodynamically homogeneous melt. Relevant correlations are found between lf dynamics and some involved structure quantities such as the cage volume around Ni atoms, Omega Ni, or the Theta Ni parameter which reflects the geometry of the nearest-neighbor cage around Ni atoms. Further, at 810 K there is a weak correlation between heterogeneous dynamics and fluctuations of the mean potential energy per atom and a comparable weak anticorrelation with the particle density and Ni-atom density inhomogeneities, where these three correlations decrease with decreasing temperature. The present results indicate the existence of long-living regions of enhanced Omega Ni in the structure, which may act as regions of preferential initiation of irreversible lf dynamics and slow relaxation.