Long-range correlations in a locally driven exclusion process

We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in long-range density-density correlation in its stationary state. In dimensions d > 1 we show that in the thermodynamic limit this correlation decays as C(r,s)∼(r(2)+s(2))(-d) at large distances r and s away from the drive with |r - s| ≫ 1. This is derived using an electrostatic analogy whereby C(r,s) is expressed as the potential due to a configuration of electrostatic charges distributed in 2d dimension. At bulk density ρ=1/2 we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and it is argued numerically to be valid at higher orders.