Abstract
Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump l sites ahead with the probability pl approximately 1l/sigma+1 is studied by Monte Carlo simulations and the domain-wall approach. For sigma>1 the standard TASEP phase diagram is recovered, but the density profiles display additional features when 1<sigma<2. At the first-order transition line, the domain wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a sigma -dependent exponent. Within the sigma<or=1 regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit sigma=-1.
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