Matrix product solution for a partially asymmetric 1D lattice gas with a free defect

Abstract

A one-dimensional, driven lattice gas with a freely moving, driven defect particle is studied. Although the dynamics of the defect are simply biased diffusion, it disrupts the local density of the gas, creating nontrivial nonequilibrium steady states. The phase diagram is derived using mean field theory and comprises three phases. In two phases, the defect causes small localized perturbations in the density profile. In the third, it creates a shock, with two regions at different bulk densities. When the hopping rates satisfy a particular condition (that the products of the rates of the gas and defect are equal), it is found that the steady state can be solved exactly using a two-dimensional matrix product ansatz. This is used to derive the phase diagram for that case exactly and obtain exact asymptotic and finite size expressions for the density profiles and currents in all phases. In particular, the front width in the shock phase on a system of size $L$ is found to scale as $L^{1/2}$, which is not predicted by mean field theory. The results are found to agree well with Monte Carlo simulations.

20 pages, 5 figures

References in corpus (4)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Shocks in the asymmetric exclusion process with internal degree of freedom
• Driven tracers in narrow channels
• Power series method for solving TASEP-based models of mRNA translation

Cited by in corpus (5)

• Milestoning estimators of dissipation in systems observed at a coarse resolution: When ignorance is truly bliss
• Macroscopic fluctuations of a driven tracer in the symmetric exclusion process
• Integrability of two-species partially asymmetric exclusion processes
• Current fluctuations in a partially asymmetric simple exclusion process with a defect particle
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle