Volume 58, Number 4, May 2002
|Page(s)||482 - 488|
|Published online||01 May 2002|
Superdiffusive Klein-Kramers equation: Normal and ano malous time evolution and Lévy walk moments
Department of Physics, Massachusetts Institute of
Technology 77 Massachusetts Avenue, Room 12-109, Cambridge,
MA 02139, USA
2 NORDITA - Blegdamsvej 17, DK-2100 København Ø, Denmark
3 Theoretische Polymerphysik, Universität Freiburg Hermann-Herder-Str. 3, 79104 Freiburg i.Br., Germany
4 Institut für Physik, Humboldt-Universität zu Berlin Invalidenstr. 110, 10115 Berlin, Germany
Accepted: 15 February 2002
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.
PACS: 05.40.Fb – Random walks and Lévy flights / 05.60.Cd – Classical transport / 02.50.Ey – Stochastic processes
© EDP Sciences, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.