Individual colloidal particles have been studied experimentally in a one dimensional random potential with energies that follow a Gaussian distribution. This rough, noise-like potential has been realised using a holographic optical set-up, which allows the width of the distribution to be varied. For different widths, the particle trajectories were followed and the particle dynamics characterised by, for example, the mean square displacement, non-Gaussian parameter, van Hove function, time-dependent diffusion coefficient and residence time distribution. The values obtained for these observables are consistent with the static properties of the system, in particular the barrier height distribution, which was obtained by a detailed characterisation of the tweezer-like set-up. The dynamics display three distinct behaviours: at short times normal diffusion, subsequently an extended regime of localisation within the different minima of the potential and finally a very slow approach towards long-time diffusive behaviour, for which diffusion coefficients consistent with theoretical predictions have been found.

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.

T he dynamics of dilute suspensions of charged polyslyrene sphercs have heen studied in a sinusoidal potential. Wc invcstigated experimclllally and theoretically (he elreel of the wavelength and amplitude of this potential as weil as the partieIe sizc on the mcnn square displacemenl, the distribution of displacemeuls and the non··Gaussian parameter. These propcl'ties seale with thc radius of the particles and the magnitude of the waveveetor 01' the potential as expected frorn a dimensional analysis. In contrast, they show a non-trivial dependel\ce on the amplitude of tJle potential, which determines the barrier height encoul\tei"ed in long-distance motiolls and also the intermediate-time dynamics in the potential weil. The periodic potential leads to particle dynamies which resemble the self dynamics of variolls systems approaching their glass transition. In pnrticular, we found thaI the timc-dependent mean sq uare displacements detennined in ollr system are surprisingly close to the ones in a quasi twodimensional colloidal supercooled liquid . In this case, the role of Ihe colloid volUlnc fraction is played by the amplitude of the potential. The similat"ity of the menn sq uare di splacements is partieularly striking sinee an individual eolloidlll particle in a periodic potential represen ts a considerably simpler si tuation than a highly concentrated multi-particle sys tem .

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.

Using Monte Carlo simulations, individual Brownian particles have been investigated in a one-dimensional random energy landscape whose energy levels are selected from a Gaussian distribution. The standard deviation of the distribution determines the roughness of the noise-like potential and was varied in the simulations. After initialization, which was done by an instantaneous or infinitely slow (annealed) quench, the particle dynamics were followed. They were characterized by a number of parameters, such as the mean squared displacement, the time dependent diffusion coefficient, the non-Gaussian parameter, and the van Hove function. The dynamics exhibit different regimes: at very short times superdiffusion, followed by normal diffusion, and subsequently an extended period of subdiffusive dynamics due to localization within the minima of the potential, and finally, after a very slow approach towards the long-time limit, again diffusion with a significantly reduced diffusion coefficient. The long-time diffusion coefficient is consistent with theoretical predictions while no predictions exist for the intermediate times. Nevertheless, over the whole time range, the simulation results are in agreement with recent experimental findings on colloidal particles in a random potential created by a holographic optical setup.