Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion

Abstract

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.

15 pages, no figures, discussions expanded

References in corpus (3)

• Stability of Tsallis antropy and instabilities of Renyi and normalized Tsallis entropies: A basis for q-exponential distributions
• Anomalous diffusion and Tsallis statistics in an optical lattice
• Anomalous diffusion, nonlinear fractional Fokker-Planck equation and solutions

Cited by in corpus (6)

• A simple mathematical model for anomalous diffusion via Fisher's information theory
• Strong Decays of the Orbitally Excited Scalar $D_0^{\ast }$ Mesons
• Strong decays analysis of excited nonstrange charmed mesons: Implications for spectroscopy
• Hamiltonian formulation of fractional kinetics
• Asymptotic symmetries in an optical lattice
• Rates of $D_0^{\ast }(2400)$, $D_J^{\ast }(3000)$ as the $D_0^{\ast }(2P)$ and $D_0^{\ast }(3P)$ in $B$ Decays