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

Abstract

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 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-neighbour covariances, finding a remarkable agreement between mean-field and simulation results. The stationary state phase diagram is mapped out analytically at the mean-field 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.

Figures (15)

• Figure 1: Kinetic schemes of TASEP-LR (top) and TASEP-LK with detachment only (bottom). It is assumed that lattice nodes are ordered from left to right, and the rate of each process is denoted by a corresponding symbol. The hopping process has unit rate if the arrival node is empty, or it is forbidden (zero rate) otherwise.
• Figure 2: Stationary density profile (top panel) and covariances (bottom panel) in the LD phase: ${\alpha = 0.2}$, ${\beta = 0.3}$. Colored lines denote KMC results. A black dashed line represents the MF continuum density profile, defined by equation eq:fase_LD_prof.
• Figure 3: Right boundary layer of the LD stationary density profile in figure \ref{['fig:LD_density']}. Solid colored lines denote KMC results. A red dashed line represents the exact boundary layer of an "equivalent" pure TASEP in the thermodynamic limit (see the text for details).
• Figure 4: Same as figure \ref{['fig:LD_density']} in the HD phase: ${\alpha = 0.9}$, ${\beta = 0.2}$. The black dashed line (MF continuum density profile) is defined by equation eq:fase_HD_prof.
• Figure 5: Same as figure \ref{['fig:LD_boundary_log']} for the left boundary layer of the HD phase: ${\alpha = 0.9}$, ${\beta = 0.2}$, bulk profile $\rho(x)$ defined by eq:fase_HD_prof. Note that the effective pure TASEP starts at node ${l = 2}$.