Ayyer Arvind, Roy Dipankar
Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India.
Sci Rep. 2017 Oct 19;7(1):13555. doi: 10.1038/s41598-017-12768-8.
The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram: dynamical expulsion when the density of a species becomes zero throughout the system, and dynamical localisation when the density of a species is nonzero only within an interval far from the boundaries. We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.
非对称排斥过程是一种理想化的输运随机模型，其精确解为非平衡统计物理的一般理论提供了重要见解。在这项工作中，我们考虑在一维晶格上与储库接触的具有多种粒子的完全非对称排斥过程。我们推导出了该系统在长时间极限下的精确非平衡相图。我们在相图的某些区域发现了两个新现象：当一种粒子在整个系统中的密度变为零时的动态排斥，以及当一种粒子的密度仅在远离边界的一个区间内非零时的动态局域化。我们使用所谓的嵌套胖激波对相图的宏观特征给出了完整解释。
