论文标题
在随机重置下进行二维运动的主动布朗运动
Active Brownian Motion in two-dimensions under Stochastic Resetting
论文作者
论文摘要
我们研究了在两个空间维度的随机重置的情况下，活性棕色粒子（ABP）的位置分布。我们考虑三种不同的重置协议：（i）粒子的位置和方向是重置的，（ii）只有位置是重置的，而（iii）仅重置具有一定速率$ r的方向。使用续订方法，我们在限制案例中精确计算了固定的边缘位置分布，当重置率$ r $比ABP的旋转扩散常数$ d_r $大得多或小得多。我们发现，在某些情况下，出于较大的重置速率，位置分布在重置点附近差异。差异的性质取决于特定协议。对于定向的重置，没有静止状态，但是该运动从短时间的弹道上变成了后期的扩散。我们使用扰动方法表征了短期非高斯边际位置分布。
We study the position distribution of an active Brownian particle (ABP) in the presence of stochastic resetting in two spatial dimensions. We consider three different resetting protocols : (I) where both position and orientation of the particle are reset, (II) where only the position is reset, and (III) where only the orientation is reset with a certain rate $r.$ We show that in the first two cases the ABP reaches a stationary state. Using a renewal approach, we calculate exactly the stationary marginal position distributions in the limiting cases when the resetting rate $r$ is much larger or much smaller than the rotational diffusion constant $D_R$ of the ABP. We find that, in some cases, for a large resetting rate, the position distribution diverges near the resetting point; the nature of the divergence depends on the specific protocol. For the orientation resetting, there is no stationary state, but the motion changes from a ballistic one at short-times to a diffusive one at late times. We characterize the short-time non-Gaussian marginal position distributions using a perturbative approach.
