Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles

Driven diffusive systems constitute paradigmatic models of nonequilibrium physics. Among them, a driven lattice gas known as the asymmetric simple exclusion process (ASEP) is the most prominent example for which many intriguing exact results have been obtained. After summarising key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian ASEP (BASEP) as a related class of driven diffusive system with continuous space dynamics. In the BASEP, driven Brownian motion of hardcore-interacting particles through one-dimensional periodic potentials is considered. We study whether current–density relations of the BASEP can be considered as generic for arbitrary periodic potentials and whether repulsive particle interactions other than hardcore lead to similar results. Our findings suggest that shapes of current–density relations are generic for single-well periodic potentials and can always be attributed to the interplay of a barrier reduction, blocking, and exchange symmetry effect. This implies that in general up to five different phases of nonequilibrium steady states are possible for such potentials. The phases can occur in systems coupled to particle reservoirs, where the bulk density is the order parameter. For multiple-well periodic potentials, more complex current–density relations are possible, and more phases can appear. Taking a repulsive Yukawa potential as an example, we show that the effects of barrier reduction and blocking on the current are also present. The exchange symmetry effect requires hardcore interactions, and we demonstrate that it can still be identified when hardcore interactions are combined with weak Yukawa interactions. The robustness of the collective dynamics in the BASEP with respect to variations of model details can be a key feature for a successful observation of the predicted current–density relations in actual physical systems.

Cluster mean-field dynamics in one-dimensional TASEP with inner interactions and Langmuir dynamics

In the area of statistical physics, totally asymmetric simple exclusion process (TASEP) is treated as one of the most important driven-diffusive systems. It contains profound non-equilibrium statistical physics mechanisms due to being the paradigm model like Ising model. Different with previous work, a one-dimensional TASEP coupled with inner interactions and Langmuir dynamics is taken into account. Weak coupled binding and unbinding rates are introduced in the proposed model. Bond breaking and making mechanisms of self-driven particles illustrating the unidirectional movement of protein motors are investigated by means of performing cluster mean-field analyses. Dynamics in the proposed system dominated by the competition between the attraction effect and the repulsion one are found to depend on the specific value of the interaction energy of these active particles. The research work will be helpful for understanding non-equilibrium statistical behaviors of interacting particle systems.