Jeon Jae-Hyung, Metzler Ralf
Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021147. doi: 10.1103/PhysRevE.85.021147. Epub 2012 Feb 27.
Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.
单粒子追踪已成为研究扩散特性的标准工具，尤其适用于诸如生物细胞等小系统。通常，所得时间序列是根据各个轨迹的时间平均值进行分析的。在此，我们研究由分数布朗运动和分数朗之万方程建模的受限正态扩散以及反常扩散，并表明即使对于此类遍历系统，时间平均量与其系综平均量的行为也有所不同，无论测量时间有多长。因此，了解时间平均值的精确行为对于正确地从物理角度解释测量的时间序列至关重要，特别是对于从数据中提取弛豫时间尺度而言。
