Exact solution of the facilitated totally asymmetric simple exclusion process. (4th December 2019) - Goldstein, S; Lebowitz, J L; Speer, E R
Abstract: We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle at site j   in jumps, at integer times, to site j    +  1, provided site j    −  1 is occupied and site j    +  1 is empty. When started with a Bernoulli product measure at density, the system approaches a stationary state. This non-equilibrium steady state (NESS) has phase transitions at and . The different density regimes, , and exhibit many surprising properties; for example, the pair correlation satisfies, for all, , with k   =  2 when, k   =  6 when, and k   =  3 when . The quantity, where is the variance in the number of particles in an interval of length L, jumps discontinuously from to 0 when and when .