Dynamical phase transition of a 1D transport process including death

Abstract

Motivated by biological aspects related to fungus growth, we consider the competition of growth and corrosion. We study a modification of the totally asymmetric exclusion process, including the probabilities of injection $\alpha$ and death of the last particle $\delta$. The system presents a phase transition at ${\delta }_c(\alpha )$, where the average position of the last particle $<L>$ grows as $\sqrt{t}$. For $\delta >{\delta }_c$, a non equilibrium stationary state exists while for $\delta <{\delta }_c$ the asymptotic state presents a low density and max current phases. We discuss the scaling of the density and current profiles for parallel and sequential updates.

4 pages, 5 figures