临界点附近非互易与奇守恒动力学中的标度行为
Scaling behavior in non-reciprocal and odd conserved dynamics near criticality
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中文总结 AI 辅助
本研究采用微扰动力学重整化群技术，探究非互易Cahn-Hilliard模型临界点附近的标度行为，发现结构与动力学关联遵循不同标度律，其结果或对生命系统调控相分离有重要启示。
中文摘要 AI 辅助
近年来，非互易性被作为微观尺度非平衡活动的普遍表现，在各类活性物质系统中得到探索，涵盖化学活性酶混合物、胶体、液滴，以及工程化光控活性胶体、机器人超材料等。描述具有非互易相互作用的守恒物种二元混合物动力学的常用最小模型为非互易Cahn-Hilliard（NRCH）模型。该模型以类温度调谐参数为特征，可触发相分离；其非互易耦合可导致时空图案形成，因为它代表非平衡活动的内在来源，且打破宇称与时间反演对称性。本研究采用微扰动力学重整化群技术，探究临界点附近NRCH模型的标度行为。研究发现，结构与动力学关联由不同关联长度控制，二者均在临界点发散，但遵循不同标度律：结构关联始终由温度及经典Wilson-Fisher临界指数控制，而动力学关联长度呈现多个标度 regime，其中温度或非互易耦合均可作为关键调谐参数占主导，且存在新的临界指数表征其发散。该临界点对应具有奇迁移率的类平衡守恒动力学，记为奇Cahn-Hilliard（OCH）模型。研究结果或对生命系统如何利用催化反应速率及整体代谢作为控制参数，调控相分离与时空图案形成具有重要启示。
英文摘要
In recent years, non-reciprocity has been explored as a ubiquitous manifestation of non-equilibrium activity at the microscopic scales for various active matter systems, from mixtures of chemically active enzymes, colloids, and droplets, to engineered light-controlled active colloids and robotic meta-materials. A commonly used minimal model to describe the dynamics of a binary mixture of conserved species with non-reciprocal interactions is the non-reciprocal Cahn-Hilliard (NRCH) model. The model is characterized by a temperature-like tuning parameter, which can trigger phase separation, and a non-reciprocal coupling, which can lead to the formation of spatio-temporal patterns, as it represents an intrinsic source of non-equilibrium activity and breaks parity and time-reversal symmetries. Here, we study the scaling behavior of the NRCH model near the critical point using perturbative dynamical renormalization group techniques. We find that structural and dynamical correlations are controlled by different correlation lengths, both of which diverge at the critical point, but governed by different scaling laws. In particular, while the structural correlations are always controlled by temperature and the classical Wilson-Fisher critical exponent, the dynamical correlation length exhibits multiple scaling regimes in which either temperature or non-reciprocal coupling can dominate as the key tuning parameter, with a new critical exponent characterizing the divergence. The critical point corresponds to a conserved equilibrium-like dynamics with odd mobility, which we denote as the odd Cahn-Hilliard (OCH) model. Our findings may have important implications on how living systems can control phase separation and spatio-temporal pattern formation using the rates of catalytic reactions, and in general metabolism, as control parameters.
