Abstract
We consider diffusion of a particle in rearranging environment, so that the diffusivity of the particle is a stochastic function of time. In our previous model of “diffusing diffusivity” [Jain and Sebastian, J. Phys. Chem. B 120, 3988 (2016)], it was shown that the mean square displacement of particle remains Fickian, i.e., at all times, but the probability distribution of particle displacement is not Gaussian at all times. It is exponential at short times and crosses over to become Gaussian only in a large time limit in the case where the distribution of in that model has a steady state limit which is exponential, i.e., . In the present study, we model the diffusivity of a particle as a Lévy flight process so that has a power-law tailed distribution, viz., with . We find that in the short time limit, the width of displacement distribution is proportional to , implying that the diffusion is Fickian. But for long times, the width is proportional to which is a characteristic of anomalous diffusion. The distribution function for the displacement of the particle is found to be a symmetric stable distribution with a stability index which preserves its shape at all times.
- Received 17 November 2016
- Revised 27 February 2017
DOI:https://doi.org/10.1103/PhysRevE.95.032135
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