标题： 相互作用活性浴中的示踪动力学：涨落与能量分配 显示英文标题

标题： Tracer dynamics in an interacting active bath: fluctuations and energy partition

摘要： 我们研究了与相互作用活性浴耦合的大质量示踪粒子的动力学，将其建模为过阻尼活性粒子的谐振链，旨在理解浴的相互作用和活性对示踪粒子非平衡涨落的影响。从微观方程出发，我们推导出示踪粒子的有效朗之万方程，并从浴中得到耗散力和随机力。我们分析了摩擦核函数，在弱耦合极限下揭示出幂律尾部，在强耦合情况下表现出指数衰减。由于浴的相互作用、探针-浴耦合和活性之间的相互作用，均方位移、速度以及稳态速度关联展现出不同的动力学区域，我们对其进行了解析表征。在谐波约束下，我们发现能量分布在一个低活性时成立但在高活性时失效，动能表现出一种关于浴活性的非单调依赖关系。 显示英文摘要

摘要： We investigate the dynamics of a massive tracer particle coupled to an interacting active bath, modeled as a harmonic chain of overdamped active particles analytically, with an aim to understand the impact of bath interactions and activity on the nonequilibrium fluctuations of the tracer. From the microscopic equations, we derive the tracer particle's effective Langevin equation, obtaining the dissipative and stochastic forces from the bath. We analyze the friction kernel, revealing power-law tails in the weak coupling limit and exponential decay in the strong coupling regime. Due to the interplay between bath interactions, probe-bath coupling, and activity, the mean squared displacement, velocity, and stationary velocity correlations exhibit different dynamical regimes, which we characterize analytically. Under harmonic confinement, we find that energy equipartition holds at low activity but breaks down at higher activity, with the kinetic energy exhibiting a non-monotonic dependence on the activity of the bath.