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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 summarizing key findings, including the mapping of the ASEP to quantum spin chains, we discuss the recently introduced Brownian asymmetric simple exclusion process (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.
Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the the average current, the situation is much less understood for higher statistics. In this pa
Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic constants.
Single-file transport in pore-like structures constitute an important topic for both theory and experiment. For hardcore interacting particles, a good understanding of the collective dynamics has been achieved recently. Here we study how softness in
We study two interacting identical run and tumble particles (RTPs) in one dimension. Each particle is driven by a telegraphic noise, and in some cases, also subjected to a thermal white noise with a corresponding diffusion constant $D$. We are intere
We present a comprehensive study of the phase transitions in the single-field reaction-diffusion stochastic systems with field-dependent mobility of a power-low form and the internal fluctuations. Using variational principles and mean-field theory it