Non-Markovian Levy diffusion in nonhomogeneous media

Details Non-Markovian Levy diffusion in nonhomogeneous media Non-Markovian Levy diffusion in nonhomogeneous media

2006-11-02

arxiv.org/abs/cond-mat/0611056v2

Phys. Rev. E75, (2007) 051105

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2 figures

Scientific paper

10.1103/PhysRevE.75.051105

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.

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