Permittivity Perturbation theory

Ya.B. applied formal perturbation theory to the interaction of an atom with the electrons of a metal, where the latter are assumed to be free. Meanwhile, Casimir and Polder and Lifshitz neglected the spatial dispersion of the dielectric permittivity of the metal. Therefore, in the region of small distances, frequencies of order ui0 are important at small distances in the sense indicated above, as are arbitrarily small frequencies at large distances. In both limits the dielectric permittivity of the metal is not at all close to one. Meanwhile, the perturbation theory used by Ya.B. corresponds formally to an expansion in powers of e - 1. and is therefore not applicable in this case. Neglecting the spatial dispersion is valid, however, only at distances r > a (a is the Debye radius in the metal) of the atom from the surface. At the opposite extreme, r a, the wave vectors kj 1/r > a vF/u>0 Me of importance (vF is the electron speed at the Fermi boundary). In this region of strong spatial dispersion perturbation theory can be applied, and the (--dependence satisfies Zeldovich s law. 

X. Gonze and C. Lee, "Dynamical matrices, Bom effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory," Phys. Rev. B 55 (1997), 10355-10368. 

All the important contributions to the forces between molecules arise ultimately from the electrostatic interactions between the particles that make up the two molecules. Thus our main theoretical insight into the nature of intermolecular forces comes from perturbation theory, using these interactions as the perturbation operator H = Z e, /(4jtSor/y), where is the charge on particle i in one molecule, is the distance between particles i and / in different molecules, and 8q is permittivity of a vacuum. The definitions of the contributions, such as the repulsion, dispersion, and electrostatic terms, which are normally included in model potentials, correspond to different terms in the perturbation series expansion. 

In the perturbation theory, we assume that the magnetic field vector hy of a surface plasmon supported by a general planar waveguide with and without the refractive index profile perturbation is described by Eq. 18. For the unperturbed and perturbed waveguide with permittivity profiles e(x) and s(x) = s(x) + Ss(x), respectively, this equation can be rewritten as ... 

A classical resonance-absorption theory [66, 67] was aimed to obtain the formulas applicable for calculation of the complex permittivity and absorption recorded in polar gases. In the latter theory a spurious similarity is used between, (i) an almost harmonic perturbed law of motion of a charge affected by a parabolic potential (ii) and the law of motion of a free rotor, this law being expressed in terms of the projection of a dipole moment onto the direction of an a.c. electric field. 

The sensor sensitivity equation for the acoustoelectric interaction can be derived from an extension of the perturbation method of Auld (Section 4.6.1). The electrical properties of liquid are represented by the relative permittivity and conductivity, a. An approximate theory for the acoustoelectric interaction has been derived by Kondoh et al. [21,22,38,48,54-56] assuming a nonconductive liquid as reference. 

Let us nov/ consider the perturbation of water structure by solutes there are three distinct types of solutes. First of all, let us discuss ions M X H20. We would like to study the environment of an ion in solution, the hydration shell. We also want to study the interaction between ions in solutions, including their hydration shells. The classical theories, based on the Debye-Huckel formalism, only deal in electrostatics, and therefore the solvent continuum only has one property, a dielectric permittivity. 

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