| Issue |
Europhys. Lett.
Volume 58, Number 4, May 2002
|
|
|---|---|---|
| Page(s) | 482 - 488 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i2002-00421-1 | |
| Published online | 01 May 2002 | |
Superdiffusive Klein-Kramers equation: Normal and ano malous time evolution and Lévy walk moments
1
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
Received:
8
October
2001
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
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