论文标题
布朗运动在高维度的非传闻重置下
Brownian motion under non-instantaneous resetting in higher dimensions
论文作者
论文摘要
我们认为，当粒子返回原点以恒定速度发生时，在更高维度重置的布朗运动。我们在此过程中研究了概率密度函数（PDF）和于点位移（MSD）的行为。我们研究了两种不同的重置协议：重置事件（泊松重置）和固定时间间隔（确定性重置）之间的指数分布时间间隔。此外，我们讨论了PDF在返回速度方面不变性的一般问题，如泊松重置的一维系统中所观察到的那样，并表明这种一维情况是唯一可以找到这种不变性的情况。但是，仍然可以在更高的维度中观察到MSD的不变性。
We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals between the resetting events (Poissonian resetting) and resetting at fixed time intervals (deterministic resetting). We moreover discuss a general problem of the invariance of the PDF with respect to the return speed, as observed in the one-dimensional system for Poissonian resetting, and show, that this one dimensional situation is the only one in which such an invariance can be found. However, the invariance of the MSD can still be observed in higher dimensions.
