发表机构
Saarland University（萨尔兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究揭示活性浴中探针的机械功率传递由浴粒子轨迹统计决定，提出轨迹-响应关系，并证明不同活性粒子模型的正功率传递条件，为预测探针响应提供新途径。
AI 中文摘要
在活性浴中移动探针的机械响应既反映浴的动力学，也反映探针与浴的耦合方式。对于以速度 $\mathbf V$ 运动并与理想活性浴弱相互作用的探针，我们证明自由浴粒子的轨迹统计决定了一个密度响应，由此可得出浴对探针的力。探针-粒子相互作用决定了该响应在波矢 $\mathbf q$ 上的加权方式，而探针运动则选择频率 $\omega_{\mathbf q}=\mathbf q\cdot \mathbf V$。这一轨迹-响应关系将浴动力学与波矢加权分离，因此无需针对每种探针相互作用和速度重新计算稳态或力关联。将此关系应用于活性粒子模型，我们证明：对于所有维度下的 active Ornstein--Uhlenbeck 粒子和 $d\geq2$ 维度下的 complete-reset run-and-tumble 粒子，正功率传递被排除；而一维 run-and-tumble 粒子和二维 active Brownian 粒子则拥有可传递正机械功率的模式。对于给定探针，该响应预测了阻力反转、自发探针运动以及运动引起的密度畸变，所有这些均与模拟定量一致。改变探针几何形状会改变同一浴响应的加权方式，从而选择不同的运动状态。在领先的弱探针、理想浴极限之外，探针强度的高阶项涉及多区间轨迹统计，而有限密度修正则涉及相互作用粒子动力学。我们的结果将活性浴粒子的轨迹统计与被动探针的机械响应联系起来，提供了一条从无探针时测得的单粒子轨迹统计来预测探针响应的途径。
英文摘要
The mechanical response of a moving probe in an active bath reflects both the dynamics of the bath and how the probe couples to it. For a probe moving at velocity $\mathbf V$ and interacting weakly with an ideal active bath, we show that the trajectory statistics of a free bath particle determine a density response from which the bath force on the probe follows. The probe-particle interaction determines how this response is weighted over wave vector $\mathbf q$, while the probe motion selects frequencies $ω_{\mathbf q}=\mathbf q\cdot \mathbf V$. This trajectory-response relation separates the bath dynamics from the wave-vector weighting, so neither the stationary state nor force correlations need to be recalculated for each probe interaction and velocity. Applying this relation to active-particle models, we prove that positive power transfer is excluded for active Ornstein--Uhlenbeck particles in all dimensions and for complete-reset run-and-tumble particles in $d\geq2$, while one-dimensional run-and-tumble particles and two-dimensional active Brownian particles possess modes that can transfer positive mechanical power. For a given probe, this response predicts drag reversal, spontaneous probe motion, and motion-induced density distortions, all in quantitative agreement with simulations. Varying the probe geometry changes how the same bath response is weighted, thereby selecting different moving states. Beyond the leading weak-probe, ideal-bath limit, higher orders in probe strength involve multi-interval trajectory statistics, while finite-density corrections involve interacting-particle dynamics. Our results connect the trajectory statistics of active bath particles to the mechanical response of a passive probe, providing a route to predict probe response from single-particle trajectory statistics measured in the absence of the probe.
Comments30 pages, 9 figures
