engleski

Disordered exclusion process with long-range hopping

We study the effect of a single defect site in the long-range generalization of the asymmetric exclusion process where particles are allowed to jump any distance l ≥ 1 with the probability that decays as l−(1+sigma). In the case of a single defect we find two regimes, separated by sigma_c = 4/3, corresponding to the presence and the absence of shocks. Furthermore, we show that the mean-field approximation describes well the non-trivial σ-dependent power-law behavior of density profiles. [1] We also investigate the relevance of disorder in the same model. Contrary to the standard (short-range) case where disorder is always relevant and induces a plateau in the current-density relation, we find the regime in σ such that for 1 < σ < σ_d the current-density relation without a plateau is restored. We discuss on the value of σd. [1] J. Szavits-Nossan and K. Uzelac, J. Stat. Mech. P12019 (2009)

ASEP; excusion process; phase transitions out of equilibrium

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