Dynamical patterns in active-passive particle mixtures with non-reciprocal interactions: Exact hydrodynamic analysis

James Mason, Robert L. Jack, Maria Bruna
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Abstract

The formation of dynamical patterns is one of the most striking features of non-equilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as non-reciprocal interactions. These non-equilibrium phenomena are challenging for modern theories. Here, we introduce a model mixture of active (self-propelled) and passive (diffusive) particles with non-reciprocal effective interactions, which is amenable to exact mathematical analysis. We exploit state-of-the-art methods to derive exact hydrodynamic equations for the particle densities. We study the resulting collective behavior, including the linear stability of homogeneous states and phase coexistence in large systems. This reveals a novel phase diagram with the spinodal associated with active phase separation protruding through the associated binodal, heralding the emergence of dynamical steady states. We analyze these states in the thermodynamic limit of large system size, showing, for example, that sharp interfaces may travel at finite velocities, but traveling phase-separated states are forbidden. The model's mathematical tractability enables precise new conclusions beyond those available by numerical simulation of particle models or field theories.
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具有非互惠相互作用的主动-被动粒子混合物的动力学模式:精确流体力学分析
动力学模式的形成是非平衡物理系统最显著的特征之一。最近的研究表明,这种模式一般产生于违反牛顿第三定律的力,即所谓的非互惠相互作用。这些非平衡现象对现代理论提出了挑战。在这里,我们介绍了一种具有非互斥效应相互作用的主动(自推进)和被动(扩散)粒子的混合模型,它可以进行精确的数学分析。我们利用最先进的方法推导出粒子密度的精确流体力学方程。我们研究了由此产生的集体行为,包括均相态的线性稳定性和大系统中的相共存。这揭示了一种新颖的相图,其中与活动相分离相关的自旋二项式突出于相关的二项式,预示着动态稳定态的出现。我们分析了大系统规模热力学极限下的这些状态,举例说明尖锐界面可以以有限速度移动,但禁止移动相分离状态。该模型在数学上的可操作性使得它能够得出精确的新结论,而这些结论是粒子模型或场理论的数值模拟所无法获得的。
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