期刊
JOURNAL OF STATISTICAL PHYSICS
卷 190, 期 3, 页码 -出版社
SPRINGER
DOI: 10.1007/s10955-022-03036-9
关键词
Stochastic lattice gases; Simple exclusion process; Self-diffusion; Cross-diffusion system; Method of matched asymptotics
In this study, we investigate a two-species simple exclusion process on a periodic lattice and derive evolution equations for the two population densities using the method of matched asymptotics in the dilute regime. Our results capture non-trivial interaction terms neglected in the mean-field approach and generalize the rigorous hydrodynamic limit to the case of unequal rates. We also obtain a cubic polynomial approximation of the self-diffusion coefficient that agrees well with numerical simulations and the Taylor expansion.
We consider a two-species simple exclusion process on a periodic lattice. We use the method of matched asymptotics to derive evolution equations for the two population densities in the dilute regime, namely a cross-diffusion system of partial differential equations for the two species' densities. First, our result captures non-trivial interaction terms neglected in the mean-field approach, including a non-diagonal mobility matrix with explicit density dependence. Second, it generalises the rigorous hydrodynamic limit of Quastel (Commun Pure Appl Math 45(6):623-679, 1992), valid for species with equal jump rates and given in terms of a non-explicit self-diffusion coefficient, to the case of unequal rates in the dilute regime. In the equal-rates case, by combining matched asymptotic approximations in the low-and high-density limits, we obtain a cubic polynomial approximation of the self-diffusion coefficient that is numerically accurate for all densities. This cubic approximation agrees extremely well with numerical simulations. It also coincides with the Taylor expansion up to the second-order in the density of the self-diffusion coefficient obtained using a rigorous recursive method.
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