Fractional Langevin equation.

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion that enable us to distinguish these two non-Markovian processes.

• Publication year

  2001

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2001-03-06

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.64.051106arXiv cond-mat/0103128PMID 11735899
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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