Totally asymmetric simple exclusion process on a periodic lattice with Langmuir kinetics depending on the occupancy of the forward neighboring site

We generalize the totally asymmetric simple exclusion process with Langmuir kinetics on aperiodic lattice. In the extended model, the rates of attachment and detachment depend onthe occupancy of the forward neighboring site. Using a mean-field theory, we obtain theanalytical expression of the density profile in the steady state and the relaxationdynamics in our model. We verify their accuracy by comparing the results with Monte Carlosimulations.