Totally asymmetric simple exclusion process with local resetting and open boundary conditions

We study a totally asymmetric simple exclusion process with open boundary conditions and local resetting at the injection node. We investigate the stationary state of the model, using both mean-field (MF) approximation and kinetic Monte Carlo simulations, and identify three regimes, depending on the way the resetting rate scales with the lattice size. The most interesting regime is the intermediate resetting one, as in the case of periodic boundary conditions. In this regime we find pure phases and phase separation phenomena, including a low-density/high-density phase separation, which was not possible with periodic boundary conditions. We discuss density profiles, characterizing bulk regions and boundary layers, and nearest-neighbor covariances, finding a remarkable agreement between MF and simulation results. The stationary state phase diagram is mapped out analytically at the MF level, but we conjecture that it may be exact in the thermodynamic limit. We also briefly discuss the large resetting regime, which exhibits an inverse characteristic length scale diverging logarithmically with the lattice size.