Effect of detachments in asymmetric simple exclusion processes
The authors consider a one-dimensional lattice model with \(N\) lattice sites, where particles enter and leave the system at boundary points with two different (flux) rates, taking values in the unit square. In this model each lattice site \(i\) is either occupied by a particle, or empty, and the only allowed motion is that of particles hopping from site \(i\) one step forward to site \(i+1\). In addition particles can dissociate irreversibly with rate \(q\) (dissociation rate). Without the detachments (\(q=0\)) the model is reduced to a totally asymmetric simple exclusion model for which the exact solution is known. The authors argue that their system can be represented as two totally asymmetric exclusion processes (AEPs) over two sublattices with effective fluxes, coupled at a certain site, and stationary particle currents through the sublattices are related by special conditions. According to them, the current through the right sublattice should be equal to the current through the left sublattice minus the current lost due to the irreversible dissociation. Since each sublattice can be viewed independently and AEP has three stationary phases, there are nine stationary phases of the considered process. The authors give the description of the phases in terms of the flux, dissociation rates and values of currents through the sublattices. The Monte Carlo simulation allows the authors to suggest that: for \(q<\frac{1}{2}\) there are five stationary phases, while for \(q>\frac{1}{2}\) there are only four of them. The reading of the paper is difficult for mathematicians since the authors do not give an analytical expression for the generator of the considered stochastic process prior and after the thermodynamic limit.
scientific article; zbMATH DE number 1903937