Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities
Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities
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DOI：
10.1103/physrevx.7.021002
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发表时间：
2017-04-05
影响因子：
12.5
通讯作者：
Sokolov, Igor M.
中科院分区：
文献类型：
--
作者：
Chechkin, Aleksei V.;Seno, Flavio;Sokolov, Igor M.
越来越多的生物，软，活性物质系统被观察到表现出正常的扩散动力学的均方位移的线性增长，但与非高斯分布的增量。基于Chubinsky-Slater的扩散系数概念，本文建立并分析了具有波动扩散系数的扩散过程的最小模型框架。特别是，我们证明了等效的扩散扩散过程与超统计方法的扩散率分布，在时间短于扩散相关时间。在较长的时间，交叉到高斯分布与有效的扩散率出现。具体来说，我们建立了布朗但非高斯扩散过程的从属图片，它可以用于广泛的一类扩散率波动统计。我们的结果被证明是在很好的协议与模拟和数值评估。
A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations.