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Special Issue:
TOPICAL REVIEW — Statistical Physics and Complex Systems
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| TOPICAL REVIEW—Statistical Physics and Complex Systems |
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Sub-diffusive scaling with power-law trapping times |
| Luo Liang (罗亮)a, Tang Lei-Han (汤雷翰)a b |
a Beijing Computational Science Research Center, Beijing 100084, China;
b Department of Physics and Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Hong Kong, China |
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Abstract Thermally driven diffusive motion of a particle underlies many physical and biological processes. In the presence of traps and obstacles, the spread of the particle is substantially impeded, leading to subdiffusive scaling at long times. The statistical mechanical treatment of diffusion in a disordered environment is often quite involved. In this short review, we present a simple and unified view of the many quantitative results on anomalous diffusion in the literature, including the scaling of the diffusion front and the mean first-passage time. Various analytic calculations and physical arguments are examined to highlight the role of dimensionality, energy landscape, and rare events in affecting the particle trajectory statistics. The general understanding that emerges will aid the interpretation of relevant experimental and simulation results.
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Received: 08 April 2014
Revised: 29 May 2014
Accepted manuscript online:
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PACS:
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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05.40.Fb
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(Random walks and Levy flights)
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66.10.C-
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(Diffusion and thermal diffusion)
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87.16.dp
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(Transport, including channels, pores, and lateral diffusion)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175013) and the Research Grants Council of the Hong Kong Special Administrative Region, China (Grant No. N HKBU 213/10). |
Corresponding Authors:
Tang Lei-Han
E-mail: lhtang@csrc.ac.cn
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| About author: 05.40.-a; 05.40.Fb; 66.10.C-; 87.16.dp |
Cite this article:
Luo Liang (罗亮), Tang Lei-Han (汤雷翰) Sub-diffusive scaling with power-law trapping times 2014 Chin. Phys. B 23 070514
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