极端持久活性物质中的无标度关联
Scale-free correlations in extremely persistent active matter
AI总结：
本文研究极端持久活性物质，分析低密度小游泳速度极限下的活性布朗粒子系统，推导其密度与速度关联的无标度代数衰减规律，经数值模拟及Claude工具验证。
AI中文摘要：
无标度关联被认为是非平衡系统的普遍特征，但其明确推导较为罕见且常涉及近似。本文分析了低密度、小游泳速度极限下的无限持久活性布朗粒子系统，发现密度和游泳速度关联均按r^{-(d+1)}代数衰减（d=2时带有对数修正）；在倒易空间中，这些关联表现为k=0处的尖点。分析预测通过数值模拟得到证实，结果通过与Claude（Opus 4.8、5及Fable 5）交互获得并经作者验证。
英文摘要：
Scale-free correlations are believed to be generic in out of equilibrium systems but their explicit derivations are rare and often involve approximations. Here we analyze a system of infinitely persistent active Brownian particles in the low density and small-swim-velocity limit. We show that both the density and swim velocity correlations decay algebraically as r^{-(d+1)} (with logarithmic corrections in d=2). In reciprocal space these correlations manifest themselves as cusps at k=0. The analytical predictions are confirmed by numerical simulations. The results were obtained through interaction with Claude (Opus 4.8 and 5, and Fable 5) and verified by the author.
