Asymmetric Exclusion Process with Global Hopping

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We study a one-dimensional totally asymmetric simple exclusion process with one special site from which particles fly to any empty site (not just to the neighboring site). The system attains a non-trivial stationary state with density profile varying over the spatial extent of the system. The density profile undergoes a non-equilibrium phase transition when the average density passes through the critical value 1-1/[4(1-ln 2)]=0.185277..., viz. in addition to the discontinuity in the vicinity of the special site, a shock wave is formed in the bulk of the system when the density exceeds the critical density.