  We study the dynamics of condensation in a misanthrope process with nonlinear
jump rates and factorized stationary states. For large enough density, it is
known that such models have a phase separated state, with a non-zero fraction
of the total mass concentrating in a single lattice site. It has been
established in [B Waclaw and M R Evans, Phys. Rev. Lett., 108(7):070601, 2012]
for asymmetric dynamics that such processes exhibit explosive condensation,
where the time to reach the stationary state vanishes with increasing system
size. This constitutes a spatially extended version of instantaneous gelation
which has previously been studied only in mean-field coagulation models. We
show that this phenomenon also occurs for symmetric dynamics in one dimension
if the non-linearity is strong enough, and we find a coarsening regime where
the time to stationarity diverges with the system size for weak non-linearity.
In higher space dimensions explosive condensation is expected to be generic for
all parameter values. Our results are based on heuristic mean field arguments
which are confirmed by simulation data.
