Max Planck Institute for the Physics of Complex Systems: New paper

We have a new paper published in Phys Rev E that explains how one can use Langevin equations to describe various regimes of anomalous superdiffusive behavior:

(October 29, 2012)

“Langevin description of superdiffusive Levy processes”

The description of diffusion processes is possible in different frameworks such as random walks or Fokker- Planck or Langevin equations. Whereas for classical diffusion the equivalence of these methods is well established, in the case of anomalous diffusion it often remains an open problem. In this paper we aim to bring three approaches describing anomalous superdiffusive behavior to a common footing. While each method clearly has its advantages it is crucial to understand how those methods relate and complement each other. In particular, by using the method of subordination, we show how the Langevin equation can describe anomalous diffusion exhibited by Levy-walk-type models and further show the equivalence of the random walk models and the generalized Kramers-Fokker-Planck equation. As a result a synergetic and complementary description of anomalous diffusion is obtained which provides a much more flexible tool for applications in real-world systems.

Visit the Publications page for a link to the paper.