Phase transition and phase coexistence in coupled rings with driven exclusion processes

We study one-dimensional exclusion processes in two coupled closed rings consisting of a common diffusive channel and two parallel active (driven) channels. Our model displays bulk-driven phase transition and phase coexistence in the form of a localized domain wall (DW) in one of the active channels in a limit where the diffusive and driven dynamics compete. By controlling a splitting parameter which tunes the in-coming currents into the active channels, the system can be brought to a delocalization transition, when delocalized DWs are formed in both the active channels. We characterize the DW fluctuations numerically.