# Long-range correlations in a locally driven exclusion process

### Tridib Sadhu 1 Satya N. Majumdar 2 David Mukamel 3

#### Physical Review E, American Physical Society, 2014, 90, pp.012109

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 $C(r,s)\sim (r^2+s^2)^{-d}$ 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 $\rho=1/2$ 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 is argued numerically to be valid at higher orders.

• 1. IPHT - Institut de Physique Théorique (ex SPhT)
• 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
• 3. Weizmann Institute