RT Journal Article
T1 Continuous time random walks in periodic systems: fluid limit and fractional differential equations on the circle
A1 Calvo, Iván
A1 Carreras, Benjamín A.
A1 Sánchez, Raúl
A1 Van Milligen, Boudewijn Ph.
AB In this paper, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Lévy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann–Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.
PB Institute of Physics
SN 1751-8113
YR 2007
FD 2007-11-09
LK https://hdl.handle.net/10016/8898
UL https://hdl.handle.net/10016/8898
LA eng
NO 12 pages, 1 figure.-- PACS nrs.: 05.40.Fb, 02.50.Ey, 05.60.Cd, 05.10.Gg.-- ArXiv preprint available at: http://arxiv.org/abs/0708.3213
NO Research sponsored by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2004-04319. Part of this research was sponsored by the Laboratory Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle,LLC, for the US Department of Energy under contract number DE-AC05-00OR22725.
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RD 27 jul. 2024