Time-averaged Einstein relation and fluctuating diffusivities for the Levy walk

被引：71

作者：

Froemberg, D. ^{[1
]}

Barkai, E. ^{[1
]}

机构：

[1] Bar Ilan Univ, Dept Phys, Inst Nanotechnol & Adv Mat, IL-52900 Ramat Gan, Israel

来源：

PHYSICAL REVIEW E | 2013年 / 87卷 / 03期

基金：

以色列科学基金会;

关键词：

ANOMALOUS DIFFUSION;

D O I：

10.1103/PhysRevE.87.030104

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The Levy walk model is a stochastic framework of enhanced diffusion with many applications in physics and biology. Here we investigate the time-averaged mean squared displacement (delta(2)) over bar often used to analyze single particle tracking experiments. The ballistic phase of the motion is nonergodic and we obtain analytical expressions for the fluctuations of (delta(2)) over bar. For enhanced subballistic diffusion we observe numerically apparent ergodicity breaking on long time scales. As observed by Akimoto [Phys. Rev. Lett. 108, 164101 (2012)], deviations of temporal averages delta(2) from the ensemble average < x(2)> depend on the initial preparation of the system, and here we quantify this discrepancy from normal diffusive behavior. Time-averaged response to a bias is considered and the resultant generalized Einstein relations are discussed. DOI: 10.1103/PhysRevE.87.030104

引用

页数：5

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