Exact solution of the facilitated totally asymmetric simple exclusion process

• Published in: Journal of statistical mechanics Vol. 2019; no. 12; pp. 123202 - 123211
• Main Authors: Goldstein, S, Lebowitz, J L, Speer, E R
• Format: Journal Article
• Language: English
• Published: IOP Publishing and SISSA 04.12.2019
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/ab363f

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 .