Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

Details Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

2007-08-23

arxiv.org/abs/0708.3213v2

J. Phys. A: Math. Theor. 40 (2007) 13511-13522

Physics

Condensed Matter

Statistical Mechanics

14 pages, 1 figure. References added. Published version

Scientific paper

10.1088/1751-8113/40/45/002

In this article, 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 Levy 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.

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