Steady states in a model of opposing local and nonlocal hops

We study a one-dimensional lattice model of particles following hard-core exclusion and performing opposing local and nonlocal moves with probability p and 1-p, respectively. Our model shows the interesting feature that the direction of the particle current can be switched by simply changing the density ρ of particles on the lattice. We study the dependence of current on p as well as ρ and present the separation of positive and negative current regions on a p-ρ plane. Further, we study the effect of disorder on this model by introducing a single site with valvelike dynamics. The site allows only unidirectional, local outward motion with rate r. The interplay of the disorder strength r, particle density ρ, and probability p leads to a rich possibility with four different kinds of shock phases in the steady state. We study the shock densities using Monte Carlo simulations and mean field calculations. While our mean field treatment describes the numerical results quite well qualitatively, we see certain quantitative deviations. We try to understand these deviations using measures of correlation in the system and provide heuristic arguments for the mismatch.