Hopping and microscopic dynamics of ultrasoft particles in cluster crystals

We have investigated the slow dynamics of ultrasoft particles in crystalline cluster phases, where point particles interact through the generalized exponential potential u(r) = \epsilon \exp[-(r/\sigma)^n], focusing on the cluster fcc phase of this model with n=4. In an effort to elucidate how the mechanisms of mass transport depend on the microscopic dynamics and in order to mimic a realistic scenario in a related experiment we have performed molecular dynamics, Brownian dynamics, and Monte Carlo simulations. In molecular dynamics simulations the diffusion of particles proceeds through long-range jumps, guided by strong correlations in the momentum direction. In Monte Carlo and Brownian dynamics simulations jump events are short-ranged, reflecting the purely configurational nature of the dynamics. In contrast to what was found in models of glass-forming liquids, the effect of Newtonian and stochastic microscopic dynamics on the long-time relaxation cannot be accounted for by a temperature-independent rescaling of the time units. From the obvious qualitative discrepancies in the short time behavior between the three simulation methods and the non-trivial difference in jump length distributions, long time relaxation, and dynamic heterogeneity, we learn that a more complex modeling of the dynamics in realistic systems of ultrasoft colloids is required.