标题： 耦合粘弹性介质中的异常扩散：分数阶朗之万方程方法 显示英文标题

标题： Anomalous diffusion in coupled viscoelastic media: A fractional Langevin equation approach

摘要： 异常扩散常常出现在复杂环境中，其中粘弹性或拥挤条件会影响粒子的运动。 在许多生物和软物质系统中，介质的不同组分表现出独特的粘弹性响应，导致观察到的扩散指数随时间变化。 在此，我们建立了一个两个粒子的理论模型，每个粒子嵌入在不同的粘弹性介质中，并通过谐波势耦合。 通过构建并求解带有记忆指数$0<\alpha<\beta\leq 1$的耦合分数阶朗之万方程（FLEs）系统，我们揭示了由记忆核和双线性耦合相互作用引起的丰富瞬态异常扩散现象。 值得注意的是，我们识别出恢复动力学，其中一种亚扩散粒子（$\alpha$）暂时加速并最终恢复其固有的长时间流动性。 这种恢复仅在记忆指数不同时出现（$\alpha<\beta$），而相同的指数（$\alpha=\beta$）会抑制恢复。 我们的理论预测为实验中观察到的瞬态异常扩散提供了见解，例如聚合物-蛋白质复合物和交联的细胞骨架网络，突显了记忆异质性和机械相互作用在生物异常扩散中的关键作用。 显示英文摘要

摘要： Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic responses, resulting in time-dependent changes in the observed diffusion exponents. Here, we develop a theoretical model of two particles, each embedded in a distinct viscoelastic medium, and coupled via a harmonic potential. By formulating and solving a system of coupled fractional Langevin equations (FLEs) with memory exponents $0<\alpha<\beta\leq 1$, we uncover rich transient anomalous diffusion phenomena arising from the interplay of memory kernels and bilinear coupling. Notably, we identify recovery dynamics, where a subdiffusive particle ($\alpha$) transiently accelerates and eventually regains its intrinsic long-time mobility. This recovery emerges only when memory exponents differ ($\alpha<\beta$), whereas identical exponents ($\alpha=\beta$) suppress recovery. Our theoretical predictions offer insight into experimentally observed transient anomalous diffusions, such as polymer--protein complexes and cross-linked cytoskeletal networks, highlighting the critical role of memory heterogeneity and mechanical interactions in biological anomalous diffusion.