Thoughts about Anomalous Diffusion: Time-Dependent Coefficients versus Memory Functions
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Electrons and holes in a semiconducting device , interstitial atoms injected into a solid , molecules in a gas container, ink droplets in a glass of liquid, mice carrying the deadly Hantavirus over a landscape , all of these entities engage in a common activity: they diffuse. The study of diffusion has, therefore, been fundamental, important, and active in diverse disciplines. Famous thinkers who have made primary and oft-used contributions to such a study include not only the physicist Einstein  but the financial expert Bachelier , the former in his research on Brownian motion, the latter during his investigations of markets and stock movements. In the present manuscript, the authors report thoughts and calculations regarding two manners of the generalization of the fundamental process of diffusion. Such generalization becomes necessary when the mechanism of motion is more complex than in normal diffusion and may involve coherence, spatial restrictions, trapping, and similar features.
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