Continuous-time random walk theory of superslow diffusion

Details Continuous-time random walk theory of superslow diffusion Continuous-time random walk theory of superslow diffusion

2010-10-05

arxiv.org/abs/1010.0782v1

Europhys. Lett. 92, 30001 (2010)

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1209/0295-5075/92/30001

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this behavior of the variance occurs when the complementary cumulative distribution function of waiting times is asymptotically described by a slowly varying function. In this case, we derive a general representation of the laws of superslow diffusion for both biased and unbiased versions of the model and, to illustrate the obtained results, consider two particular classes of waiting-time distributions.

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