Sep 2 – 7, 2018
Europe/Warsaw timezone

Brownian Asymmetric Simple Exclusion Process

Sep 6, 2018, 3:00 PM


Dominik Lips (Universität Osnabrück, Germany)


We present a model of a Brownian asymmetric simple exclusion process (BASEP) with underdamped Brownian Dynamics, which is an extension on the well-known asymmetric simple exclusion process (ASEP) defined on a discrete lattice. In the BASEP, particles of size $\sigma$ with hardcore interaction are driven by a constant drag force through a one-dimensional cosine potential with period $\lambda$. The amplitude of the cosine potential is much larger than $k_{\rm\scriptscriptstyle B} T$, leading to an effective hopping motion of particles between potential wells. Under periodic boundary conditions, the system reaches a non-equilibrium steady-state (NESS) with a constant particle current. In general, the character of these NESS is strikingly different from the one in the ASEP. Compared to the particle current in a system of non-interacting particles, we observe an enhancement for small $\sigma/\lambda$ ratios, caused by a barrier reduction effect arising from multi-occupation of potential wells. Larger ratios lead to a suppression of the current because of strong blocking effects. Surprisingly, an exchange-symmetry effect leads to a current-density relation identical to that of non-interacting particles for the commensurable length $\sigma=\lambda$. A current-density relation similar to the ASEP is obtained only for a limited parameter regime. The rich behavior of the current-density relation is reflected in non-equilibrium phase-diagrams for open-systems, which can exhibit up to five phases. The topology of these phase diagrams changes with varying $\sigma/\lambda$ ratio. We furthermore discuss transition times and splitting probabilities for a tagged particle in the BASEP. These quantities exhibit a remarkable asymmetry, which we relate to the collective particle motion in the NESS.

Primary author

Dominik Lips (Universität Osnabrück, Germany)


Dr Artem Ryabov (Charles University) Prof. Philipp Maass (Universität Osnabrück, Germany)

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