R. J. Concannon, R. A. Blythe
We investigate a non-Poissonian version of the asymmetric simple exclusion process, motivated by the observation that motor proteins hop as a consequence of some internal dynamics which yields a non-Markovian (history-dependent) hopping process. We characterize a large family of processes using a waiting-time distribution for individual particle hops. We find that when the variance of this distribution 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 are both rather subtle, and depends on how the microscopic dynamics subsequent to a failed particle hop attempt are defined.
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http://arxiv.org/abs/1307.7511
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