Jeon Jae-Hyung, Chechkin Aleksei V, Metzler Ralf
Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
Phys Chem Chem Phys. 2014 Aug 14;16(30):15811-7. doi: 10.1039/c4cp02019g.
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 〈x(2)(t)〉 ≃ 2K(t)t with K(t) ≃ 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.
反常扩散通常用标度布朗运动（SBM）来描述，它是一种高斯过程，其扩散系数随时间呈幂律变化。其均方位移为〈x(2)(t)〉≃2K(t)t，其中对于0 < α < 2，K(t)≃t(α - 1)。在无界扩散的情况下，SBM可能提供一个看似充分的描述，此时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，自由的SBM是弱非遍历的，但时间平均均方位移没有显著的幅度散射。更严重的是，我们证明在受限情况下，SBM编码的动力学与分数布朗运动和连续时间随机游走在根本上是不同的。SBM是高度非平稳的，不能为处于热平衡静止系统中的粒子提供物理描述。我们的发现对单粒子追踪实验的建模有直接影响，特别是在细胞隔室内受限的情况下或使用光镊追踪方法时。
