Classical Driven Transport in Open Systems with Particle Interactions and General Couplings to Reservoirs

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.

Figure 1

Sketch of the model and illustration of the particle injection for (a) the bulk-adapted and (b) the equilibrated-bath couplings. Right reservoirs are not shown.

Figure 2

Steady-state density profiles for $V=2V_c$ from KMC simulations (symbols) in comparison with the TDFT predictions (lines). For the KMC results averages were performed over ${10}^9$ particle jumps in the steady state. The inset shows the density profile for the equilibrated-bath couplings close to the left and right boundary, respectively.

Figure 3

Phase diagrams of the NESS for (a) the bulk-adapted and (b) the equilibrated-bath couplings at $V=2V_c$. KMC results for the phase transitions are marked by the symbols and TDFT results by the lines (solid lines for first-order and dashed lines for second-order phase transitions). In (a) seven phases are obtained, where the bulk density ${\rho }_B$ equals either the reservoir densities ${\rho }_L$ or ${\rho }_R$, or the value 0.5 in the minimum current phase, or the two possible values ${\rho }_{\max ,1}$ or ${\rho }_{\max ,2}$ in the maximum current phases. In (b) a maximum current phase with ${\rho }_B={\rho }_{\max ,1}$, a minimum current phase with ${\rho }_B=0.5$, and three phases with reservoir-controlled densities ${\rho }_B=f_{\mathrm{I}}({\rho }_L)$, ${\rho }_B=f_{\mathrm{III}}({\rho }_R)$, and ${\rho }_B=f_{\mathrm{V}}({\rho }_R)$ are obtained, where the different functions of ${\rho }_L$ or ${\rho }_R$ are determined from the simulated or calculated density profiles. The labeling by roman numbers in (a) and (b) has been chosen in such a manner that corresponding phases have equal numbers.