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arXiv 2602.21134cond-mat.soft
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通过随机重置控制惯性主动布朗运动

Controlling inertial active Brownian motion via stochastic resetting

Institute of Physics(印度物理研究所);Homi Bhabha National Institute(霍米·巴巴国立大学);Department of Physics, University of Vermont(佛蒙特大学物理系)

Manish Patel, Amir Shee

AI总结:

本文研究了通过随机重置控制惯性主动布朗运动,揭示了惯性对重置控制输运的显著影响,包括增强局部化和非高斯稳态特征。

摘要:

惯性是许多生物和合成主动系统固有的特性,从动物和机器人代理到胶体游动体,惯性强烈地塑造了输运。许多此类系统采用间歇性重启协议来调节探索。随机重置提供了一种理论框架来这些策略,并提供了一条控制非平衡稳态的途径,但重置控制主动动力学中惯性的作用仍不明确。本文研究了一个受二维完全随机重置位置、速度和方向影响的惯性主动布朗粒子。利用动量生成框架以及终值定理,我们推导出闭合形式的稳态矩,直到四阶,作为惯性、活动性和重置率的函数。我们证明惯性从根本上改变了重置控制的输运:在大重置率下,稳态均方位移的抑制比过阻尼极限更强烈,导致在重置点附近增强的局部化。同时,位置超额偏度相图揭示了具有明显中心峰和重尾的强非高斯稳态,表明由惯性持续性允许的罕见长游动。尾部重量随重置率非单调变化,反映了惯性动量松弛和重置之间的竞争,选择了一个最大化罕见游动的最优区域。我们的结果为重置控制主动系统中惯性效应提供了实验可检验的特征。

英文摘要:

Inertia is intrinsic to many living and synthetic active systems, from animals and robotic agents to colloidal swimmers, and it strongly shapes transport. Many such systems employ intermittent restart protocols to regulate exploration. Stochastic resetting provides a theoretical framework for these strategies and a route to control nonequilibrium steady states, yet the role of inertia in reset-controlled active dynamics remains poorly understood. Here we study an inertial active Brownian particle in two dimensions under complete and partial stochastic resetting. We derive exact stationary second- and fourth-order scalar moments for the different protocols wherever their stationary limits exist, and obtain the full transient evolution of the mean-squared velocity and displacement under complete resetting. Under complete resetting, inertia strongly enhances localization: at large reset rates, the steady-state mean-squared displacement decays as $r^{-3}$, rather than following the overdamped scaling $r^{-1}$. Kurtosis-based phase diagrams reveal strongly non-Gaussian position and velocity statistics, including activity-induced re-entrant behavior as a function of reset rate and inertia. The transient solutions show that resetting shifts the velocity-relaxation rates, whereas the terminal relaxation of the displacement is governed solely by the mean resetting time $1/r$, with inertia controlling the faster transient modes. Comparing complete resetting with the partial protocols, we find that resetting the velocity together with the position substantially enhances localization. Resetting the orientation to a fixed or a random direction drives the mean-squared velocity toward opposite limits. These results establish inertia, reset frequency, and the choice of reset variables as coupled control parameters for localization, relaxation, and non-Gaussian fluctuations in active systems.

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。

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