Role of site-wise dynamic defects in a resource-constrained exclusion process

Abstract

We study an exclusion process with site-wise dynamic disorder in a resource constrained environment. The dynamic defects that hinder the particle flux on the lattice stochastically appear and disappear throughout the lattice with a constrained binding rate and a constant unbinding rate, respectively. The effect of constrained resources on the stationary properties of the system has been comprehended in the form of the filling factor. The analytical results replicated by naive mean-field theory accord quite well with the Monte Carlo simulation for faster defects irrespective of the affected hopping rate and slower defects with a large affected hopping rate. For slower defects with a small affected hopping rate, some correlations are observed in the system, leading to the adoption of an enhanced mean-field approach which provides reasonably better approximations than the usual naive-mean field. These correlations slowly fade away with an increase in the affected hopping rate. Our theoretical calculations unify the parameters – the affected hopping rate, defect binding (unbinding) rate, and defect density – that control defect kinetics on the lattice into a single parameter known as the obstruction factor. The repercussions of the obstruction factor have been thoroughly examined by discussing its limiting cases. The phase boundaries that are yielded through different mean-field approaches are uniquely impacted by their corresponding obstruction factor.