Bulk-Driven Nonequilibrium Phase Transitions in a Mesoscopic Ring

We study a periodic one-dimensional exclusion process composed of a driven and a diffusive part. In a mesoscopic limit where both dynamics compete we identify bulk-driven phase transitions. We employ mean-field theory complemented by Monte Carlo simulations to characterize the emerging nonequilibrium steady states. Monte Carlo simulations reveal interesting correlation effects that we explain phenomenologically.

Figure 1

Schematic model of the ring system. The dynamics of the upper (passive) lane with lattice sites ${\tilde{x}}_i$ is governed by a SEP with rate $D$, and the dynamics of the lower (active) lane with lattice sites $x_i$ by a TASEP with unity jump rate.

Figure 2

Simulated density profiles of the active part in a system of $N=500$ and $n_p=0.38$ for different diffusion strengths $d$ (indicated in the graph). The system is in the LD-HD phase featuring a domain wall. With increasing $d$ the domain wall position (intersection with the solid line) is shifted to the left [see Eq. (5)] and DW fluctuations increase. The left boundary layers are due to current limitation caused by correlations at the passive part boundaries (see text).

Figure 3

Phase diagram obtained by MF (solid lines) exhibits four phases. Simulations [MC (triangles) and LD-HD (circles) phase boundaries, $N=200$] reveal a failure of the MF analysis: correlations at the passive part boundaries cause a diminished current that shifts the MC phase.