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Nonequilibrium Transport and Phase Transitions in Driven Diffusion of Interacting Particles
Zeitschrift für Naturforschung A ( IF 1.8 ) Pub Date : 2020-05-26 , DOI: 10.1515/zna-2020-0028
Dominik Lips 1 , Artem Ryabov 2 , Philipp Maass 1
Affiliation  

Abstract 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.

中文翻译:

相互作用粒子驱动扩散中的非平衡输运和相变

摘要 驱动扩散系统构成了非平衡物理的范式模型。其中,被称为不对称简单排除过程 (ASEP) 的驱动晶格气体是最突出的例子,已经获得了许多有趣的精确结果。在总结了关键发现之后,包括 ASEP 到量子自旋链的映射,我们讨论了最近引入的布朗 ASEP(BASEP)作为具有连续空间动力学的驱动扩散系统的相关类别。在 BASEP 中,考虑了通过一维周期势驱动的核心相互作用粒子的布朗运动。我们研究了 BASEP 的电流-密度关系是否可以被视为适用于任意周期势,以及硬核以外的排斥粒子相互作用是否会导致类似的结果。我们的研究结果表明,电流-密度关系的形状对于单井周期势是通用的,并且总是可以归因于势垒减少、阻塞和交换对称效应的相互作用。这意味着,对于这种势能,一般来说,最多五个不同的非平衡稳态阶段是可能的。相可以出现在耦合到粒子库的系统中,其中体积密度是顺序参数。对于多阱周期势,更复杂的电流-密度关系是可能的,并且可以出现更多的相。以排斥汤川势为例,我们表明势垒减少和阻塞对电流的影响也存在。交换对称效应需要核心交互,我们证明,当核心交互与弱汤川交互相结合时,它仍然可以被识别。BASEP 中集体动力学相对于模型细节变化的稳健性可能是成功观察实际物理系统中预测的电流-密度关系的关键特征。
更新日期:2020-05-26
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