Exact solution of the facilitated totally asymmetric simple exclusion process. (4th December 2019)

• Record Type: Journal Article
• Authors: Goldstein, S; Lebowitz, J L; Speer, E R
• Is Part Of: Journal of statistical mechanics. (2019:Dec.)
• Publication Date: 2019-12-04
• Subjects: 4 -- 11 -- 16; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab363f
• Languages: English
• ISSNs: 1742-5468

Abstract

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 .