活性Ornstein--Uhlenbeck粒子的持久性、重置与首次通过时间
Persistence, resetting, and first-passage times of an active Ornstein--Uhlenbeck particle
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中文总结 AI 辅助
本研究通过微扰和更新方法，分析了活性Ornstein--Uhlenbeck粒子在随机重置下的首次通过时间，发现重置可降低平均时间，并构建了参数相图。
中文摘要 AI 辅助
我们研究了在一维有限区间内，一端为吸收边界、另一端为反射边界，并受到随机重置影响的活性Ornstein--Uhlenbeck粒子的首次通过时间统计。在弱活性区域，我们发展了Fokker--Planck方程的微扰解，并利用更新框架获得了首次通过时间分布及其低阶矩的解析表达式。在没有重置的情况下，活性既可能增加也可能减少平均首次通过时间，这取决于持久时间与扩散吸收时间之间的关系。当引入重置时，我们确定了有益重置的起始点以及重置率有限范围，在此范围内重置降低了活性系统的平均首次通过时间。我们进一步表明，重置转变依赖于速度重置协议。最后，通过将带重置的活性粒子与不带重置的被动布朗粒子进行比较，我们构建了一个相图，识别出活性和重置共同降低平均首次通过时间的参数空间区域。
英文摘要
We study the first-passage time statistics of an active Ornstein--Uhlenbeck particle on a finite one-dimensional interval with an absorbing boundary at one end and a reflecting boundary at the other, subject to stochastic resetting. In the weak-activity regime, we develop a perturbative solution of the Fokker--Planck equation and use a renewal framework to obtain analytical expressions for the first-passage-time distribution and its low-order moments. In the absence of resetting, activity can either increase or decrease the mean first-passage time, depending on the relation between the persistence time and the diffusive time to absorption. When resetting is introduced, we determine both the onset of beneficial resetting and the finite range of resetting rates for which resetting lowers the mean first-passage time of the active system. We further show that the resetting transition depends on the velocity resetting protocol. Finally, by comparing the active particle with resetting to the passive Brownian particle without resetting, we construct a phase diagram that identifies the regions of parameter space in which activity and resetting together reduce the mean first-passage time.
