Coupling of two asymmetric exclusion processes with open boundaries

We study the dynamics of a coupled two-channel ASEP in which intra-channel transition rates are dependent on the configuration of neighboring channel. The binding constant k, which signifies the ratio of inter-channel transition rates, is introduced and the symmetric and asymmetric coupling conditions are analyzed for different values of k. The vertical cluster mean-field theory is used to study the system behavior exactly in strong coupling conditions and approximately in intermediate coupling conditions. Additionally, the consequences of particular dynamics such as totally asymmetric simple exclusion process (TASEP), partially asymmetric simple exclusion process (PASEP) and symmetric simple exclusion process (SSEP) in either one or both channels are investigated. It is found that the transition rates have a significant influence on both the qualitative and quantitative nature of the phase diagrams. The mathematical computation shows how the number of phases varies from 3 via 6 to 7 under different environments. Interestingly, in the fully asymmetric coupling case, the results are found to be independent of the magnitude of non-zero vertical transition rate. Our theoretical arguments are in well agreement with extensively performed Monte-Carlo simulation results.