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

We investigate the density profile in a driven diffusive system caused by a plane particle source perpendicular to the driving force. Focusing on the case of critical bulk density $\overline{c}$ we use a field theoretic renormalization group approach to calculate the density $c\left(z\right)\mathrm{}$ as a function of the distance from the particle source at first order in $\epsilon =2-d$ ($d$ denotes the spatial dimension). For $d=1\mathrm{}$ 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 $d=2\mathrm{}$ with the result $c\left(z\right)-\overline{c}\sim z^{-1\mathrm{}}{\left[\ln \mathrm{}\right(z\left)\right]}^{\frac{2}{3}}$ for $z\to \infty$.