论文标题
随机重置对带有随机扩散系数的布朗运动的影响
Effect of stochastic resetting on Brownian motion with stochastic diffusion coefficient
论文作者
论文摘要
我们研究了布朗运动的动力学，其扩散系数随机发展。我们首先以任意维度研究此过程，并找到缩放形式和位置分布的相应缩放函数。我们发现分布的尾巴具有指数式尾巴，并具有弹道缩放。然后，我们引入重置动力学，以恒定的速率，位置和扩散系数都重置为零。这最终导致非平衡固定状态，我们在任意维度上进行研究。与重置下的普通布朗运动形成鲜明对比的是，一个维度的固定位置分布在原点上具有对数差异。但是，对于更高的维度，差异消失，分布在原点处达到尺寸依赖性的恒定值，我们会准确地计算出来。该分布在所有维度上具有通用拉伸指数尾巴。 我们还研究了固定状态的方法，并发现随着时间的流逝，原点周围的内部核心区域达到了固定状态，而外部区域仍然具有瞬态分布 - 该内部固定区域的生长$ \ sim t^2 $，即具有恒定加速度，比普通的棕色运动快得多。
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position distribution. We find that the tails of the distribution have exponential tails with a ballistic scaling. We then introduce the resetting dynamics where, at a constant rate, both the position and the diffusion coefficient are reset to zero. This eventually leads to a nonequilibrium stationary state, which we study in arbitrary dimensions. In stark contrast to ordinary Brownian motion under resetting, the stationary position distribution in one dimension has a logarithmic divergence at the origin. For higher dimensions, however, the divergence disappears and the distribution attains a dimension-dependent constant value at the origin, which we compute exactly. The distribution has a generic stretched exponential tail in all dimensions. We also study the approach to the stationary state and find that, as time increases, an inner core region around the origin attains the stationary state, while the outside region still has a transient distribution -- this inner stationary region grows $\sim t^2$, i.e., with a constant acceleration, much faster than ordinary Brownian motion.
