发表机构
University of Stuttgart（斯图加特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过压力展开和重正化群方法，自底向上推导了二维活性布朗粒子及其手性变体的标量场理论，揭示了手性模型中的奇项，为活性物质流体动力学描述提供了新途径。
AI 中文摘要
活性布朗粒子（ABP）模型是标量活性流体研究中使用最广泛的基于粒子的模型之一。已知相互作用的ABP集合会表现出平衡态对应物中不存在的引人入胜的现象。一个突出的例子是自发相分离，称为运动诱导相分离（MIPS），即使在不存在显式吸引相互作用的情况下也会发生。与此同时，标量活性流体的大尺度行为通常使用连续介质描述（即标量场理论）来建模。此类标量活性场理论通常以自顶向下的方式构建，建立它们与基于粒子的模型之间的联系仍然具有挑战性，且这些联系尚未被完全理解。为了推进标量活性场理论的微观推导，我们重新审视了在二维空间中通过两体势相互作用的ABP与包含所有空间梯度最高四阶项的标量场理论之间的联系。我们的方法基于压力展开和奇异摄动理论背景下的重正化群（RG）方法。RG方法提供了一种系统的方法来消除快变量并识别慢不变流形上的动力学。在此框架内，标量场理论可以作为RG流方程获得。我们还将此方法应用于ABP模型的手性变体，即手性ABP（cABP）模型，其中恒定扭矩使粒子旋转偏向左侧或右侧。我们表明，与cABP模型对应的标量场理论除了包含ABP标量场理论中的项之外，还包含两个“奇”项。这里开发的方法也可能有助于推导其他类型活性物质系统的流体动力学描述。
英文摘要
The active Brownian particle (ABP) model is one of the most widely used particle-based models in studies of scalar active fluids. A collection of interacting ABPs is known to exhibit intriguing phenomena that are absent in equilibrium counterparts. A prominent example is spontaneous phase separation, known as motility-induced phase separation (MIPS), which occurs even in the absence of explicit attractive interactions. In parallel, the large-scale behavior of scalar active fluids is often modeled using continuum descriptions, namely, scalar field theories. Such scalar active field theories are usually formulated in a top-down manner, and establishing their connections to particle-based models remains challenging, with these connections not yet fully understood. To advance the microscopic derivation of scalar active field theories, we revisit the connection between ABPs interacting via a two-body potential in two dimensions and scalar field theories that include all possible terms up to fourth order in spatial gradients. Our approach is based on a pressure expansion and the renormalization group (RG) method in the context of singular perturbation theory. The RG method provides a systematic way to eliminate fast variables and identify the dynamics on the slow invariant manifold. Within this framework, scalar field theories can be obtained as RG flow equations. We also apply this method to a chiral variant of the ABP model, the chiral ABP (cABP) model, in which a constant torque biases particle rotation to the left or right. We show that the scalar field theory corresponding to the cABP model contains two ``odd'' terms in addition to those present in the scalar field theory for ABPs. The method developed here may also be useful for deriving hydrodynamic descriptions of other types of active matter systems.
Comments41 pages, 3 figures
