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

TL;DR

This paper uses a field theoretic renormalization group approach to analyze the particle density profile in driven diffusive systems with open boundaries, providing analytical results and comparisons with exact solutions.

Contribution

It introduces a renormalized field theory method to compute density profiles in driven diffusive systems, including logarithmic corrections at critical dimensions.

Findings

Agreement with exact solutions in one dimension

Derived density profile with logarithmic corrections in two dimensions

Calculated the asymptotic behavior of the density profile

Abstract

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 $z \rightarrow \infty$.