Lévy meets Boltzmann: Strange initial conditions for Brownian and fractional Fokker-Planck equations

Ralf Metzler, Joseph Klafter

Research output: Contribution to journalConference articlepeer-review

Abstract

We study normal and anomalous diffusion processes with initial conditions of the broad Lévy type, i.e., with such initial conditions which, per se, exhibit a diverging variance. In the force-free case, the behaviour of the associated probability density function features distinct shoulders which can be related to the probability current flowing away from the origin. In the presence of an external potential which eventually leads to the emergence of a non-trivial, normalisable equilibrium probability density function, the initially diverging variance becomes finite. In particular, the effects of strange initial conditions for the harmonic Ornstein-Uhlenbeck potential are explored to some detail. Methods to quantify the dynamics related to such kinds of processes are investigated.

Original languageEnglish
Pages (from-to)290-296
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume302
Issue number1-4
DOIs
StatePublished - 15 Dec 2001
EventInternational Workshop on Frontiers in the Physics of Complex Systems - Ramat-Gan, Israel
Duration: 25 Mar 200128 Mar 2001

Keywords

  • Fokker-Planck equation
  • Fractional Fokker-Planck equation
  • Gibbs-Boltzmann equillibrium
  • Stable initial conditions

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