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Exact shock measures and steady-state selection in a driven diffusive system with two conserved densities. (English) Zbl 1206.82064

Summary: 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.

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
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