Totally Asymmetric Simple Exclusion Process on an Open Lattice with Langmuir Kinetics Depending on the Occupancy of the Forward Neighboring Site

We have generalized the update rule of the Langmuir kinetics, which is attachment and detachment dynamics of particles, in the totally asymmetric simple exclusion process. The attachment and detachment rates in our extended model depend on the occupancy of the forward neighboring site. Although there are some extended models that consider the effect of the occupancy of the neighboring sites, our model is the first one that allows one to set the attachment and detachment rates independently without any restrictions. We have performed a mean-field analysis and obtained phase diagrams and density profiles. It is elucidated that the attachment to vacant region and detachment from congested region extend the area of the phase that accompanies a shock, i.e., a domain wall, which divides the low and high density regime. Results of Monte Carlo simulations show good agreement with the mean-field density profiles, so that the validity of the phase diagrams are verified.