  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.
