arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2402.05078cond-mat.softcond-mat.stat-mech
收藏

涨落诱导的向集体运动的一级相变

Fluctuation-Induced First Order Transition to Collective Motion

David Martin, Gianmarco Spera, Hugues Chaté, Charlie Duclut, Cesare Nardini, Julien Tailleur, Frédéric van Wijland

AI总结:

本文研究干性活性物质中自推进粒子向集体运动的转变,揭示弱涨落通过极化场质量的密度依赖与反馈机制将平均场二级转变变为一级相变,并以场论和模拟验证。

摘要:

在由具有对齐作用的自推进粒子组成的体系中,向集体运动转变的本质仍是一个长期存在争议的问题。本文聚焦干性活性物质,并表明弱涨落足以在一般意义上将平均场二级转变转化为一种“不连续的”共存情形。我们的理论说明,即使在平均场层面不存在这种效应,涨落也会诱导极化场质量对密度的依赖。进而,这种对密度的依赖触发有序化与平流之间的反馈回路,最终导致非均匀的向集体运动转变以及非均匀行进带的出现。重要的是,我们证明这种涨落诱导的一级相变既存在于度量模型中——其中粒子与有限距离内的邻居对齐,也存在于“拓扑”模型中——其中对齐基于更复杂的邻居集合构造。我们利用随机微积分解析地计算了噪声诱导的极化场质量重整化,并进一步通过单圈场论分析加以支持。最后,我们通过对涨落流体动力学以及具有 k-近邻或 Voronoi 对齐的拓扑粒子模型进行数值模拟,证实了解析预测。

英文摘要:

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a `discontinuous' coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in `topological' ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑