Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model
Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model
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DOI：
10.1088/1742-5468/2016/12/123201
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发表时间：
2016-12-01
影响因子：
2.4
通讯作者：
Yamamoto, Eiji
中科院分区：
文献类型：
--
作者：
Akimoto, Takuma;Yamamoto, Eiji
在诸如自旋玻璃系统和活细胞的无序系统中的局部扩散系数是高度不均匀的，并且可以随时间改变。这种时间依赖性和空间异质性的环境导致单粒子跟踪测量的不可再现性。在随机过程弱遍历破缺的背景下，从理论上研究了时均观测量的不可重现性。在这里，我们提供了严格的描述的平衡和非平衡扩散过程的退火渡越时间模型，这是一个异质扩散模型在活细胞。我们给出了均方位移（MSD）和相对标准偏差的时间平均MSD的平衡和非平衡的情况下的解析解。我们发现，时间平均的MSD随时间线性增长，时间平均的扩散系数本质上是随机的（不可重现），即使在非平衡状态下的长时间测量。此外，时间平均的扩散系数的分布收敛到一个普适分布，在这个意义上，它不依赖于初始条件。我们的研究结果铺平了道路的无序系统中的时间平均扩散系数的分布行为的理论理解。
Local diffusion coeffcients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the time-averaged diffusion coeffcients are intrinsically random (irreproducible) even in the long-time measurements in non-equilibrium situations. Furthermore, the distribution of the time-averaged diffusion coeffcients converges to a universal distribution in the sense that it does not depend on initial conditions. Our findings pave the way for a theoretical understanding of distributional behavior of the time-averaged diffusion coeffcients in disordered systems.