Non-conserving exclusion process with a dynamic obstacle

Abstract

Motivated by complex transport processes occurring in biological and physical systems, we study a non-conserving totally asymmetric simple exclusion process with a dynamic defect particle. The defect particle may appear or disappear stochastically and slows down the traffic of moving particles while bound to the lattice. We analyze the system in the context of mean-field approach, and investigate the steady state properties which exhibit a rich dynamic behavior. The theoretically obtained density profiles and current fully describe the phase diagram, further allowing to elucidate the effect of various dynamics individually. Depending upon non-conserving kinetics and defect dynamics, phase schema displays at most eighteen phases; in total, the system exhibits twenty-one phases. Several critical values of the kinetic rates that trigger a qualitative change in the phase diagrams are obtained using analytical arguments. The theoretical outcomes are validated through extensive Monte Carlo simulations.