# Non-equilibrium phase transitions in driven diffusion systems, by Dominik Lips and Philipp Maass (Department of Physics, Osnabrück University, Germany)

Aula Pere Pascual (5th floor Physics) 2018-11-14 11:45:00

**ABSTRACT**: Models of driven stochastic particle transport in one dimension have been applied to describe such diverse phenomena as biopolymerization, molecular motor motion along filaments, flow of molecules through nanopores, ion conduction through membrane channels, electron transport along molecular wires, and vehicular traffic. A simple lattice model, the asymmetric simple exclusion process (ASEP) appears as a basic building block in the theoretical description of these driven diffusion systems and has developed into one of the standard models for investigating non-equilibrium steady states. After an introduction to the physics of the ASEP and some model variants with the focus on non-equilibrium phase transitions [1-3], we address the question whether corresponding phenomena will occur in driven Brownian motion, making them more amenable to experimental studies.

Specifically, we introduce a model of a Brownian asymmetric simple exclusion process (BASEP) with overdamped Brownian dynamics and a setup resembling that of the ASEP on a lattice [4]. In this BASEP, particles of size σ with hardcore interaction are driven by a constant drag force through a cosine potential with period λ and an amplitude much larger than the thermal energy.

We show that the character of the non-equilibrium steady states in the BASEP is strikingly different from that in the ASEP. Compared with a system of non-interacting particles, the current is enhanced for small σ/λ ratios due to 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=nλ, n=1,2... A behavior similar as for the ASEP is obtained only in a limited parameter regime. The rich behavior of the current-density relation leads to phase diagrams of non-equilibrium steady states with up to five different phases. The structure of these phase diagrams changes with varying σ/λ ratio.

[1] M. Dierl, P. Maass, and M. Einax, Phys. Rev. Lett. 108, 060603 (2012).

[2] M. Dierl, M. Einax, and P. Maass, Phys. Rev. E 87, 062126 (2013).

[3] M. Dierl, W. Dieterich, M. Einax, and P. Maass, Phys. Rev. Lett. 112, 150601 (2014).

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