Non-local response in a lattice gas under a shear drive

TL;DR

This paper investigates how localized boundary perturbations in a non-equilibrium lattice gas cause algebraically decaying density and current profiles, revealing non-local responses characteristic of non-equilibrium systems.

Contribution

It analytically demonstrates the algebraic decay of density and current profiles caused by boundary perturbations in non-equilibrium lattice gases, including both non-interacting and simple exclusion particles.

Findings

Perturbations induce algebraic decay in density and current profiles.

Analytical derivation of power-law tails for non-interacting particles.

Analytical derivation of power-law tails for particles with simple exclusion.

Abstract

In equilibrium, the effect of a spatially localised perturbation is typically confined around the perturbed region. Quite contrary to this, in a non-equilibrium stationary state often the entire system is affected. This appears to be a generic feature of non-equilibrium. We study such non-local response in the stationary state of a lattice gas with a shear drive at the boundary which keeps the system out of equilibrium. We show that a perturbation in the form of a localised blockage at the boundary, induces algebraically decaying density and current profile. In two examples, non-interacting particles and particles with simple exclusion, we analytically derive the power-law tail of the profiles.