Ergodicity recovery of random walk in heterogeneous disordered media

doi:10.1088/1674-1056/ab8212

中国物理B ›› 2020, Vol. 29 ›› Issue (5): 50503-050503.doi: 10.1088/1674-1056/ab8212

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Ergodicity recovery of random walk in heterogeneous disordered media

Liang Luo(罗亮), Ming Yi(易鸣)

1 Department of Physics, Huazhong Agricultural University, Wuhan 430070, China;
2 Institute of Applied Physics, Huazhong Agricultural University, Wuhan 430070, China;
3 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

收稿日期:2020-02-06 修回日期:2020-03-12 出版日期:2020-05-05 发布日期:2020-05-05
通讯作者: Liang Luo E-mail:luoliang@mail.hzau.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grants Nos. 11705064, 11675060, and 91730301).

Ergodicity recovery of random walk in heterogeneous disordered media

Liang Luo(罗亮)^1,2, Ming Yi(易鸣)³

1 Department of Physics, Huazhong Agricultural University, Wuhan 430070, China;
2 Institute of Applied Physics, Huazhong Agricultural University, Wuhan 430070, China;
3 School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China

Received:2020-02-06 Revised:2020-03-12 Online:2020-05-05 Published:2020-05-05
Contact: Liang Luo E-mail:luoliang@mail.hzau.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grants Nos. 11705064, 11675060, and 91730301).

摘要/Abstract

摘要： Significant and persistent trajectory-to-trajectory variance are commonly observed in particle tracking experiments, which have become a major challenge for the experimental data analysis. In this theoretical paper we investigate the ergodicity recovery behavior, which helps clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media. The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis. The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations. The strange ergodicity recovery behavior is reported in the quenched disordered case, which arises from a localization mechanism. The first-passage approach is introduced to the ergodicity analysis for this case, of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.

关键词: anomalous diffusion, random walk, disordered systems, non-Gaussian diffusion

Abstract: Significant and persistent trajectory-to-trajectory variance are commonly observed in particle tracking experiments, which have become a major challenge for the experimental data analysis. In this theoretical paper we investigate the ergodicity recovery behavior, which helps clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media. The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis. The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations. The strange ergodicity recovery behavior is reported in the quenched disordered case, which arises from a localization mechanism. The first-passage approach is introduced to the ergodicity analysis for this case, of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.

Key words: anomalous diffusion, random walk, disordered systems, non-Gaussian diffusion

中图分类号: (Fluctuation phenomena, random processes, noise, and Brownian motion)

05.40.-a

05.40.Fb (Random walks and Levy flights) 66.10.C- (Diffusion and thermal diffusion) 87.16.dp (Transport, including channels, pores, and lateral diffusion)

罗亮, 易鸣. Ergodicity recovery of random walk in heterogeneous disordered media[J]. 中国物理B, 2020, 29(5): 50503-050503.

Liang Luo(罗亮), Ming Yi(易鸣). Ergodicity recovery of random walk in heterogeneous disordered media[J]. Chin. Phys. B, 2020, 29(5): 50503-050503.

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Ergodicity recovery of random walk in heterogeneous disordered media

Ergodicity recovery of random walk in heterogeneous disordered media

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