Distributional behavior of diffusion coefficients obtained by single trajectories in annealed transit time model

作者：Akimoto Takuma^*; Yamamoto Eiji

来源：Journal of Statistical Mechanics: Theory and Experiment , 2016, 2016(12): 123201.

DOI：10.1088/1742-5468/2016/12/123201

• diffusion
• stochastic particle dynamics
• exact results

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.

• 出版日期2016-12