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Chapter 2. Fractional electrodynamics with spatial dispersionстатья
- Автор: Tarasov V.E.
- Сборник: Handbook of Fractional Calculus with Applications. Volume 5: Applications in Physics, Part B.
- Редактор: Тарасов Василий Евгеньевич
- Том: 5
- Глава в коллективной монографии
- Год издания: 2019
- Издательство: Walter de Gruyter
- Местоположение издательства: Berlin, Germany
- Первая страница: 25
- Последняя страница: 52
- DOI: 10.1515/9783110571721-002
- Аннотация: Nonlocal electrodynamics of media with power-law spatial dispersion (PLSD) are described. Spatial dispersion is a phenomenon in which the absolute permittivity of the media depends on the wave vector. Power-law spatial dispersion is described by derivatives and integrals of noninteger orders. Fractional differential equations for the electric fields in these media are suggested. The generalizations of Coulomb’s law and Debye’s screening for power-law nonlocal media are proposed. Simple models of anomalous behavior of media with PLSD are described as nonlocal properties of power-law type. As examples, we consider electric fields of point charge and dipole in media with PLSD, infinite charged wire, uniformly charged disk, capacitance of spherical capacitor, and multipole expansion for media with PLSD. A microscopic model, which is based on fractional kinetics, is proposed to describe spatial dispersion of power-law type. The fractional Liouville equation is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The proposed fractional nonlocal electrodynamics is characterized by universal spatial behavior of electromagnetic fields in media with PLSD by analogy with the universal temporal behavior of low-loss dielectrics.
- Добавил в систему: Тарасов Василий Евгеньевич