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

12 pages, 4 figures

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• Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems
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• Phase transitions in systems possessing Shock solutions
• The Study of Shocks in Three-States Driven-Diffusive Systems: A Matrix Product Approach
• Multi shocks in Reaction-diffusion models
• Condensation and coexistence in a two-species driven model
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• Q-zero range has random walking shocks
• Connection between matrix-product states and superposition of Bernoulli shock measures
• Kardar-Parisi-Zhang universality in two-component driven diffusive models: Symmetry and renormalization group perspectives
• Multi-species reaction-diffusion models admitting shock solutions
• Relaxation time in a non-conserving driven-diffusive system with parallel dynamics