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arXiv · 1306.2026

Variational principle for fractional kinetics and the Lévy Ansatz

Sumiyoshi Abe
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Abstract

A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the Lévy Ansatz. It is shown how the whole range from subdiffusion to superdiffusion is realized by the variational solution, as a competing effect between the long waiting time and the long jump. The motion of the center of the probability distribution is also analyzed in the case of a periodic drift.

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Sumiyoshi Abe. 2013-08-27. Variational principle for fractional kinetics and the Lévy Ansatz. https://doi.org/10.1103/physreve.88.022142

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