Dynamical phase transition of a 1D transport process including death

TL;DR

This paper investigates a modified 1D exclusion process modeling biological growth and death, revealing a dynamical phase transition characterized by different long-term behaviors depending on death probability.

Contribution

It introduces a new variant of the exclusion process including death, identifying a phase transition and analyzing the scaling of density and current profiles.

Findings

Existence of a critical death probability (lpha) for phase transition.

Different asymptotic states: stationary or low density/max current phases.

Scaling laws for density and current profiles under various update schemes.

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.