| Many non-equilibrium models describing transport of some conserved quantity have been proposed so far. The best known are the zero-range process and the asymmetric simple exclusion process. They are lattice models where particles jump between adjacent sites with probability given by some hopping function. A key feature of these models is that they possess a steady state which takes a factorized form over the sites of an underlying one- or higher-dimensional lattice, on which the process is defined. For certain classes of hopping rates these models undergo a phase transition from a liquid to a condensed (jammed) state. In this talk I will discuss an extension to steady states that factorize over pairs of nodes. I will show how introduction of nearest-neighbor interactions influences the condensate which can now be either localized on a single node or extended in space. Possible applications will also be discussed. |
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