Accelerating Brownian motion: A fractional dynamics approach to fast diffusion

R. Metzler*, J. Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Superdiffusion in the sub-ballistic regime with a non-diverging mean-squared displacement is studied on the basis of a linear, fractional kinetic equation with constant coefficients which is non-local in time and leads to an exponential tail of the corresponding probability density function. It is shown that sub-ballistic superdiffusion can be regarded as ballistic motion with a memory, much as slow diffusion can be thought of as a random walk with a memory. This suggests that fractional kinetic equations are useful in describing both sub-and superdiffusion processes.

Original languageEnglish
Pages (from-to)492-498
Number of pages7
JournalEurophysics Letters
Issue number5
StatePublished - 1 Sep 2000


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