Power-law Spatial Dispersion from Fractional Liouville Equation

Abstract

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

18 pages, LaTeX

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Review of Some Promising Fractional Physical Models
• Fractional Power-Law Spatial Dispersion in Electrodynamics
• Liouville and Bogoliubov Equations with Fractional Derivatives

Cited by in corpus (3)

• Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz Type
• Fractional Liouville Equation on Lattice Phase-Space
• Generalized diffusion equation with fractional derivatives within Renyi statistics