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Global Density Profile For Particle Non-Conserving One Dimensional Transport From Renormalization Group Flows
Sutapa Mukherji1, Somendra M Bhattacharjee2
1Protein Chemistry and Technology, CSIR - Central Food Technological Research Institute, Mysore 570020, India. sutapa@cftri.res.in.
Abstract:
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 differential 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 profile. The predicted scaling form is checked against numerical solutions for finite systems.
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