Phase separation and maximum flow phase in the asymmetric exclusion process with creation and annihilation

In this paper, we have investigated the interplay of the asymmetric exclusion process (ASEP) of parallel updated rules with "Langmuir kinetics" (LK) by equipping the ASEP system with the additional feature of local particle creation at empty sites with rate omega(a) and annihilation with rate omega(d). Two slightly different models are proposed. It is shown that the phase separation may occur in both models. However, in one model, the maximum flow phase may occur but in the other model, there only exists the constant bulk density phase.