Exact Solution of the F-TASEP

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 $\mathbb{Z}$ 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 $\rho$ the system approaches a stationary state. This non-equilibrium steady state (NESS) has phase transitions at $\rho =1/2$ and $\rho =2/3$. The different density regimes $0<\rho <1/2$, $1/2<\rho <2/3$, and $2/3<\rho <1$ exhibit many surprising properties; for example, the pair correlation $g(j)=⟨\eta (i)\eta (i+j)⟩$ satisfies, for all $n\in \mathbb{Z}$, ${\sum }_{j=kn+1}^{k(n+1)}g(j)=k{\rho }^2$, with $k=2$ when $0\le \rho \le 1/2$, $k=6$ when $1/2\le \rho \le 2/3$, and $k=3$ when $2/3\le \rho \le 1$. The quantity ${\lim }_{L\to \infty }{V}_L/L$, where $V_L$ is the variance in the number of particles in an interval of length L, jumps discontinuosly from $\rho (1-\rho )$ to 0 when $\rho \to 1/2$ and when $\rho \to 2/3$.

Twelve pages, LaTeX, one figure. Revised version 4/21/2019 corrects erroneous date