TY - JOUR

T1 - Matrix product solution for a partially asymmetric 1D lattice gas with a free defect

AU - Lobaskin, Ivan

AU - Evans, Martin R

AU - Mallick, Kirone

N1 - 20 pages, 5 figures. R&P deal with publisher, UoE author is corresponding author.
Funding Information:
IL acknowledges studentship funding from EPSRC under Grant No. EP/R513209/1. The work of KM has been supported by the project RETENU ANR-20-CE40-0005-01 of the French National Research Agency (ANR). KM thanks Tomohiro Sasamoto for stimulating discussions on integrable exclusion processes, which informed this work. MRE would like to thank David Mukamel for helpful discussions.
Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.

PY - 2022/4/25

Y1 - 2022/4/25

N2 - 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 L1/2, which is not predicted by mean field theory. The results are found to agree well with Monte Carlo simulations.

AB - 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 L1/2, which is not predicted by mean field theory. The results are found to agree well with Monte Carlo simulations.

KW - asymmetric simple exclusion process

KW - driven diffusive systems

KW - exactly solvable models

KW - matrix product state

KW - nonequilibrium statistical mechanics

U2 - 10.1088/1751-8121/ac5f7a

DO - 10.1088/1751-8121/ac5f7a

M3 - Article

SN - 1751-8113

VL - 55

SP - 1

EP - 19

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 20

M1 - 205002

ER -