  Recently, it was shown that spatial correlations may have a drastic effect on
the dynamics of real-space condensates in driven mass-transport systems: in
models with a spatially correlated steady state, the condensate is quite
generically found to drift with a non-vanishing velocity. Here we examine the
condensate dynamics in the accelerate exclusion process (AEP), where spatial
correlations are present. This model is a "facilitated" generalization of the
totally asymmetric simple exclusion process (TASEP) where each hopping particle
may trigger another hopping event. Within a mean-field approach that captures
some of the effects of correlations, we calculate the phase diagram of the AEP,
analyze the nature of the condensation transition, and show that the condensate
drifts, albeit with a velocity that vanishes in the thermodynamic limit.
Numerical simulations are consistent with the mean-field phase diagram.
