奔跑翻滚粒子与随机门控目标之间的首次命中时间
First hitting times between a run-and-tumble particle and a stochastically-gated target
摘要：
我们研究了一个一维的运行和翻滚粒子和目标网站之间的可见和不可见的阶段间歇性切换的第一次击中时间统计。目标的两态动力学与粒子的运动无关，粒子只能在可见光阶段被目标吸收。当运动发生在具有反射边界的有限区域内时，我们得到了平均首中时间。考虑粒子的转弯率作为一个调整参数，我们发现，弹道运动是最好的策略，以尽量减少平均首中时间。然而，首次命中时间的相对波动是大的，并表现出非单调的行为，相对于转弯率或目标过渡率。奇怪的是，这些波动对于大多数时间可见的目标来说可能是最大的，而对于那些大多数时间不可见或在两种状态之间快速过渡的目标来说则不是。在无限线上，由于目标不连续性，第一命中时间分布的经典渐近行为$\propto t^{-3/2}$通常在中间标度状态之前，该中间标度状态变化为$t^{-1/2}$。当目标大部分时间是不可见的，特别是在低转弯速率时，这种瞬态状态的范围变得非常长。在有限和无限的几何形状，我们画出类比部分吸收问题。
英文摘要：
We study the first hitting time statistics between a one-dimensional run-and-tumble particle and a target site that switches intermittently between visible and invisible phases. The two-state dynamics of the target is independent of the motion of the particle, which can be absorbed by the target only in its visible phase. We obtain the mean first hitting time when the motion takes place in a finite domain with reflecting boundaries. Considering the turning rate of the particle as a tuning parameter, we find that ballistic motion represents the best strategy to minimize the mean first hitting time. However, the relative fluctuations of the first hitting time are large and exhibit non-monotonous behaviours with respect to the turning rate or the target transition rates. Paradoxically, these fluctuations can be the largest for targets that are visible most of the time, and not for those that are mostly invisible or rapidly transiting between the two states. On the infinite line, the classical asymptotic behaviour $\propto t^{-3/2}$ of the first hitting time distribution is typically preceded, due to target intermittency, by an intermediate scaling regime varying as $t^{-1/2}$. The extent of this transient regime becomes very long when the target is most of the time invisible, especially at low turning rates. In both finite and infinite geometries, we draw analogies with partial absorption problems.
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