Don't Forget Your Tail! A Moving Condensate Maintained by its Tail

Condensate phases, where some quantity becomes localised, are found in fundamental models of a wide variety of processes, such as in traffic flow, wealth redistribution, etc. Within the 'standard' formulation of the Zero-Range Process (ZRP), where only one unit of mass 'hops' at a time, a condensation transition is observed with the appropriate choice of hop rate. However, condensates formed in this model are static, whereas many real-world systems exhibit a moving condensate phase, such as a traffic jam. To learn more about moving condensate phases we study a model based on the ZRP where all but one of the particles on a site hop at once. We find that under these dynamics a moving strong condensate is formed at all densities $\rho$ when a hopping parameter $b$ is increased beyond a critical value $b_c$. We show using analytical and numerical approaches that the model exhibits a stable moving condensate localised over a few lattice sites.