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Effect of long-range hopping on the totally asymmetric exclusion process

Importance of the effective long-range interactions [1] appearing in asymmetric exclusion processes (ASEP) rises the questions on possible consequences that an explicit introduction of long-range effects might have on the boundary-induced phase transitions in such systems. We investigate the 1d model for % totally symmetric exclusion process TASEP generalized to allow the long-range hopping with the probability decaying with distance $l$ as $1/l^{; ; \sigma+1}; ; $. Monte Carlo studies show that with properly chosen boundary conditions the phase diagram for $\sigma>1$ remains the same as in the short-range case, but the density profiles display additional features when $1<\sigma<2$ [2]. At the first-order transition line we observe the phase separation, which can be derived analytically in terms of the domain-wall theory and shares some common features with the TASEP in presence of Langmuir kinetics [3]. In the maximum-current phase the density profile has an algebraic decay with an exponent that depends on $\sigma$ for $1<\sigma<2$ and attains the short-range value $1/2$ for $\sigma\geq 2$. We show that the same scaling exponent and its short-range limit is already present in the numerical solution of the stationary equations for the density profile in the mean-field approximation. Dynamic scaling related to the evolution towards the stationary state was also investigated. We show, by using the domain-wall theory, that the dynamical exponent $z$ on the coexistence line is equal to $2$ in the infinite-length limit. We also recover the KPZ exponent $z=3/2$ for the case of the half-filled periodic chain both by Monte Carlo simulations and by showing that the macroscopic density profile in the infinite chain evolves according to the inviscid Burgers equation, as in the short-range case.\\ [1] B. Derrida, J.Lebowitz, E.R. Speer, Phys. Rev. Lett. 87, 150601 (2001) \\ [2] J. Szavits-Nossan and K. Uzelac, Phys. Rev. E 74, 051104 (2006) \\ [3] R, Juhasz, L. Santen, J. Phys. A37, 3933 (2004)

ASEP; asymmetric exclusion process; phase transitions out of equilibrium

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