论文标题
在任意维度中运行式粒子的通用特性
Universal Properties of a Run-and-Tumble Particle in Arbitrary Dimension
论文作者
论文摘要
我们考虑在$ d $尺寸中的主动运行粒子（RTP），从原点开始，并在时间间隔$ [0，t] $上发展。我们检查了RTP动力学的三个不同模型：具有瞬时倒塌的标准RTP模型，具有瞬时运行的变体以及一个通用模型，其中倒塌和运行都是非实用的。对于每个模型，我们使用Sparre Andersen定理进行离散的随机步行，以准确计算$ x $组件不会更改为$ t $的概率，这表明它不取决于$ d $。由于此结果，我们准确地计算了其他$ x $ - 组件的属性，即最大时间和记录统计信息的分布，表明它们是通用的，即它们不依赖$ d $。此外，我们表明，如果每次翻滚后的粒子的速度$ v $是随机的，则从一般概率分布中得出。我们的发现通过数值模拟证实。这些结果中的一些已在最近的一封信中宣布[Phys。莱特牧师。 124，090603（2020）]。
We consider an active run-and-tumble particle (RTP) in $d$ dimensions, starting from the origin and evolving over a time interval $[0,t]$. We examine three different models for the dynamics of the RTP: the standard RTP model with instantaneous tumblings, a variant with instantaneous runs and a general model in which both the tumblings and the runs are non-instantaneous. For each of these models, we use the Sparre Andersen theorem for discrete-time random walks to compute exactly the probability that the $x$ component does not change sign up to time $t$, showing that it does not depend on $d$. As a consequence of this result, we compute exactly other $x$-component properties, namely the distribution of the time of the maximum and the record statistics, showing that they are universal, i.e. they do not depend on $d$. Moreover, we show that these universal results hold also if the speed $v$ of the particle after each tumbling is random, drawn from a generic probability distribution. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 124, 090603 (2020)].
