Weak and strong coupling in a two-lane asymmetric exclusion process

This paper studies a two-lane totally asymmetric simple exclusion process, in which particles could jump between the two lanes with asymmetric rates. In the weak coupling situation, the rates are inversely proportional to system size L. The appearance of localized shock in one lane and the discontinuous phase transition as revealed by Juhasz [Phys. Rev. E 76, 021117 (2007)] are also reproduced. The density profiles and phase diagrams are constructed in the hydrodynamic limit, by numerically solving the steady state equations. The phase diagram in our model exhibits asymmetry, which is different from the symmetric one in Juhasz's model. We have studied the phase boundary and discontinuous line analytically. The analytical results are in good agreement with that obtained from numerical integration. We also study the strong coupling situation, in which the lane changing rates are independent of L. Results completely different from that arising from weak coupling are presented. Furthermore, features different from that of the model presented by Pronina and Kolomeisky [Physica A 372, 12 (2006)] are revealed.