标度布朗运动：描述反常扩散的含时扩散率悖论过程
Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
摘要：
反常扩散通常用尺度布朗运动（SBM）来描述，SBM是一种具有幂律时间依赖扩散系数的高斯过程。其均方位移为$\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$，其中$\mathscr{K}(t)\simeq t^{α-1}$为$0<α<2$。在无界扩散的情形下，SBM可以提供一个似乎足够的描述，其概率密度函数与分数布朗运动的概率密度函数一致。在这里，我们表明，自由SBM是弱非遍历，但不表现出显着的振幅分散的时间平均均方位移。更严重的是，我们证明了在约束下，由SBM编码的动力学是根本不同的分数布朗运动和连续时间随机游动。SBM是高度非静止的，并且不能为热静止系统中的颗粒提供物理描述。我们的研究结果对单粒子跟踪实验的建模有直接影响，特别是在细胞室内的限制下或使用光镊跟踪方法时。
英文摘要：
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with $\mathscr{K}(t)\simeq t^{α-1}$ for $0<α<2$. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
