Global Density Profle For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows.

The totally asymmetric simple exclusion process along with particle adsorption and evaporation
kinetics is a model of boundary-induced nonequilibrium phase transition. In the continuum limit, the
average particle density across the system is described by a singular diferential equation involving
multiple scales which lead to the formation of boundary layers (BL) or shocks. A renormalization
group analysis is developed here by using the location and the width of the BL as the renormalization
parameters. It not only allows us to cure the large distance divergences in the perturbative solution for
the BL but also generates, from the BL solution, an analytical form for the global density profle. The
predicted scaling form is checked against numerical solutions for fnite systems.