Brownian asymmetric simple exclusion process

We present a model of a Brownian asymmetric simple exclusion process (BASEP) with overdamped Brownian dynamics that resembles properties of the asymmetric simple exclusion process (ASEP) on a lattice [1]. In this BASEP, particles of size σ with hardcore interaction are driven by a constant drag force through a one-dimensional cosine potential with period λ. The character of the non-equilibrium steady states in the BASEP is strikingly different from that in the ASEP. Compared to the particle current in a system of non-interacting particles, we observe an enhancement for small σ/λ ratios, caused by a barrier reduction effect arising from multi-occupation of potential wells. Larger σ/λ ratios lead to a suppression of the current because of blocking effects. Surprisingly, an exchange-symmetry effect causes the current-density relation to be identical to that of non-interacting particles for commensurable lengths σ=λ. A current-density relation similar to the ASEP is obtained only for a limited parameter regime. The rich behavior of the current-density relation leads to phase diagrams of NESS in open systems with up to five different phases. The topology of these phase diagrams changes with varying σ/λ ratio.

[1] D. Lips, A. Ryabov, P. Maass, Phys. Rev. Lett. 121, 160601 (2018)