Fractional transport equations for Lévy stable processes.

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified.

• Publication year

  2000

• Venue

  Physical Review Letters

• Publication date

  2000-10-21

• Fields of study

  Medicine, Physics

• Identifiers
  DOI 10.1103/PhysRevLett.86.2208arXiv cond-mat/0010333PMID 11289891
• 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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