Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities

TL;DR

This paper analyzes a driven 1D lattice gas with two conserved densities, identifying shock solutions with product measures, calculating shock dynamics, and deriving the hydrodynamic limit to understand steady-state selection.

Contribution

It provides the most general conditions for shock solutions with product measures and explicitly computes shock hopping rates and steady states in boundary-driven systems.

Findings

Shock solutions with step-function density profiles exist.

Shock position follows a biased random walk.

Steady states depend on boundary densities.

Abstract

We study driven 1d lattice gas models with two types of particles and nearest neighbor hopping. We find the most general case when there is a shock solution with a product measure which has a density-profile of a step function for both densities. The position of the shock performs a biased random walk. We calculate the microscopic hopping rates of the shock. We also construct the hydrodynamic limit of the model and solve the resulting hyperbolic system of conservation laws. In case of open boundaries the selected steady state is given in terms of the boundary densities.