2001/07/24 by Ralf Metzler, Igor M. Sokolov
Computer Science · Mathematics · Physics and Astronomy · #Fractional Differential Equations Solutions #Nonlinear Dynamics and Pattern Formation #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1209/epl/i2002-00421-1
published as Europhys. Lett. 58, 482 (2002) · 4 pages, REVTeX
arxiv created 2001/07/24 · openalex publication_date 2002/05/01 · arxiv updated 2015/06/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a position-dependent external force field. This equation defines lower-order moments of Lévy walks which take place in the presence of an external force field and in phase space. In the velocity coordinate, the probability density relaxes in Mittag-Leffler fashion towards the Maxwell distribution whereas in the position coordinate, no stationary solution exists and the temporal evolution of moments exhibits a competition between Brownian and anomalous contributions.