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.

中文翻译：

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随机重置条件下二维滚动和翻滚粒子

我们研究了随机重置对两个空间维度中的奔跑和翻滚粒子 (RTP) 的影响。我们考虑了一个影响 RTP 位置和方向的重置协议：以恒定速率，粒子经历位置重置到空间和方向随机化中的固定点。我们计算径向和 $x$-边际平稳状态分布，并表明虽然前者接近常数值 $r \to 0$，但后者在对数上发散为 $x \to 0$。另一方面，两个边缘分布都以远离原点的相同指数呈指数衰减。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转变。我们还研究了存在复位时 RTP 的首次通过特性，并表明复位率的优化可以最小化平均首次通过时间。我们还简要讨论了以固定方向重置到初始位置的静止状态。