Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

Details Renormalized field theory and particle density profile in driven diffusive systems with open boundaries Renormalized field theory and particle density profile in driven diffusive systems with open boundaries

1996-05-28

arxiv.org/abs/cond-mat/9605175v1

Phys. Rev. E 53 (1996) 4544-4554

Physics

Condensed Matter

32 pages, RevTex, 4 Postscript figures, to appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.53.4544

We investigate the density profile in a driven diffusive system caused by a plane particle source perpendicular to the driving force. Focussing on the case of critical bulk density $\bar{c}$ we use a field theoretic renormalization group approach to calculate the density $c(z)$ as a function of the distance from the particle source at first order in $\epsilon=2-d$ ($d$: spatial dimension). For $d=1$ we find reasonable agreement with the exact solution recently obtained for the asymmetric exclusion model. Logarithmic corrections to the mean field profile are computed for $d=2$ with the result $c(z)-\bar{c} \sim z^{-1} (\ln(z))^{2/3}$ for $z \rightarrow \infty$.

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