Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion

Details Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion

2003-07-14

arxiv.org/abs/cond-mat/0307306v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, no figures, discussions expanded

Scientific paper

10.1103/PhysRevE.69.016102

Based on the canonical formalism, the dilatation symmetry is implemented to the Fokker-Planck equation for the Wigner distribution function that describes atomic motion in an optical lattice. This reveals the symmetry principle underlying the recent result obtained by Lutz [Phys. Rev. A 67, 051402(R) (2003)] on the connection between anomalous transport in the optical lattice and Tsallis statistics in the high-energy regime.Lutz's discussion is generalized to the nonstationary case, and the condition, under which the solution distribution decays as a power law, is derived.

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