论文标题
在随机重置下的二维跑步颗粒
Run-and-Tumble particles in Two-dimensions under Stochastic Resetting
论文作者
论文摘要
我们研究了随机重置对两个空间维度的跑步和滚筒粒子（RTP）的影响。我们考虑一种重置协议，该协议既影响RTP的位置和方向：恒定速率粒子经历位置重置到空间和方向随机化的固定点。我们计算径向和$ x $ -Marginal固定状态分布，并表明，尽管前者的恒定值为$ r \ to $ \ to 0 $，但后者的对数为$ x \ to 0 $。另一方面，两个边缘分布呈指数衰减，同一指数远离原点。我们还研究了RTP的时间松弛，并表明位置分布经历了向静止状态的动态过渡。我们还研究了在重置存在下RTP的第一个段落特性，并表明重置速率的优化可以最大程度地减少平均第一个通道时间。我们还简要讨论了固定状态以固定方向重置为初始位置。
We study the effect of stochastic resetting on a run and tumble particle (RTP) in two spatial dimensions. We consider a resetting protocol which affects both the position and orientation of the RTP: with a constant rate the particle undergoes a positional resetting to a fixed point in space and orientation randomization. We compute the radial and $x$-marginal stationary state distributions and show that while the former approaches a constant value as $r \to 0$, the latter diverges logarithmically as $x \to 0$. On the other hand, both the marginal distributions decay exponentially with the same exponent far away from the origin. We also study the temporal relaxation of the RTP and show that the position distribution undergoes a dynamical transition to a stationary state. We also study the first passage properties of the RTP in the presence of the resetting and show that the optimization of the resetting rate can minimize the mean first passage time. We also give a brief discussion on the stationary states for resetting to the initial position with fixed orientation.
