Exact solution of the facilitated totally asymmetric simple exclusion process

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 .