Wang Wanli, Barkai Eli, Burov Stanislav
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel.
Entropy (Basel). 2020 Jun 22;22(6):697. doi: 10.3390/e22060697.
Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.
最近，对细胞等复杂环境以及其他玻璃态系统中随机游走的观察表明，粒子在尾部的扩散遵循空间指数衰减，而非典型的高斯分布。我们使用广泛适用的连续时间随机游走模型，并获得了传播子的大偏差描述。在微观跳跃长度分布呈指数衰减或更快衰减（即排除类 Lévy 幂律分布的跳跃长度）以及等待时间分布在短等待时间内解析的温和条件下，粒子在大距离处的扩散遵循指数衰减，并伴有对数修正。在此我们展示了跳跃事件的反聚束如何降低这种效应，而聚束和间歇性则会增强这种效应。我们采用连续时间随机游走模型的精确解来检验大偏差理论。
