Long-range steady state density profiles induced by localized drive

TL;DR

This paper demonstrates that localized driving in diffusive systems creates algebraically decaying steady-state density profiles, which can be understood through an electrostatic analogy involving dipoles, applicable even with particle interactions.

Contribution

It establishes a novel electrostatic analogy for density profiles caused by localized drives in diffusive systems, including interactions, and provides a method to determine complex profiles via superposition.

Findings

Density profiles decay algebraically away from the drive.

Electrostatic analogy maps the problem to an electric dipole potential.

Superposition principle applies for multiple driving bonds.

Abstract

We show that the presence of a localized drive in an otherwise diffusive system results in steady-state density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined self-consistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.