Spatiotemporally complete condensation in a non-Poissonian exclusion process

We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that coarse graining the interactions between particles in complex systems generically leads to a stochastic process with a non-Markovian (history-dependent) character. We characterize a large family of one-dimensional hopping processes using a waiting-time distribution for individual particle hops. We find that when its variance is infinite, a real-space condensate forms that is complete in space (involves all particles) and time (exists at almost any given instant) in the thermodynamic limit. The mechanism for the onset and stability of the condensate is rather subtle and depends on the microscopic dynamics subsequent to a failed particle hop attempt.