Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients $D\left(x\right)$ are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, $D\left(x\right)$ is considered to be centerd at the origin and the entire $x$ axis is characterized by a single scaling exponent $\alpha$. In this work we consider a spatially random scenario: in periodic intervals (“layers”) in space $D\left(x\right)$ is centerd to the midpoint of each interval. In each interval the scaling exponent $\alpha$ is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains (“layer thickness”) of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.

中文翻译：

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分层扩散景观中具有高斯色噪声的非均质扩散过程和非遍历性

具有与空间有关的扩散系数的异质扩散过程（HDP） $d（X）$在许多现实世界的系统中都可以找到它们，例如用于大分子或亚微米示踪剂在生物细胞中的扩散。在这里，我们研究了具有高斯色噪声（GCN）的淬灭无序系统中的HDP，其特征在于扩散系数具有与颗粒位置相关的幂律，并且具有空间随机的缩放指数。通常，$d（X）$ 被认为以原点和整个区域为中心 $X$ 轴以单个缩放指数为特征 $\alpha$。在这项工作中，我们考虑一个空间随机的场景：在空间的周期性间隔（“层”）中$d（X）$居中于每个间隔的中点。在每个间隔中，缩放指数$\alpha$从高斯分布中随机选择。详细分析了缩放指数变化，该分层系统中扩散系数域的周期性（“层厚度”）和GCN的相关时间的影响。我们讨论了在该系统中可实现的超扩散，亚扩散和正态扩散的机制。我们观察并量化了在该系统中出现非遍历和非高斯行为的域。我们的结果为了解由有色噪声驱动的HDP的弱遍历性破坏提供了新的见识，并潜在地应用在淬火层状系统，生物细胞和组织中扩散的典型模型系统以及地球物理系统中的扩散。