Two-particle cluster integral in the expansion of the dielectric constant

We study in detail the two-particle cluster integral in the cluster expansion for the effective dielectric constant of a suspension of spherically symmetric polarizable inclusions embedded in a uniform medium. Although our form for the integrand differs from that derived earlier by Finkel'berg and by Jeffrey, we show that the integral is equivalent. The two-body dielectric problem for particles with an arbitrary radial dependence of the dielectric constant is solved by an expansion in spherical harmonics. Numerical results for some special models illustrate the importance of multipole contributions to the effective dielectric constant.     

On the electronic contribution to the surface energy of metals

An expression for the exchange and correlation contributions to the surface energy of metals is derived using the dielectric formulation of the electron gas. The result which is obtained in the infinite barrier model for the surface is exact within the RPA and include the off-diagonal character of the response function.     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.     

Sound emission by non-isomolar combustion at low Mach numbers

This paper shows that the change in the number of moles of species during combustion can make a strong contribution to the acoustic power radiated by turbulent flames and cannot be systematically neglected. Starting from standard conservation equations, we derive an expression for the acoustic pressure radiated in the far field of a compact region of fluid where low Mach number non-isomolar combustion takes place. In this formulation, the contributions from ‘molar’ and thermal expansion appear explicitly. We also give a formulation in which the sound emission arising from purely non-stationary and from purely convective effects appear independently. As an application of the theory, we derive the acoustic power emitted by a premixed flame in the flamelet regime. Numerical evaluations show that the contribution of molar expansion to the acoustic power is between 2 and 5.6 dB (260% increase) for some common hydrocarbon-oxygen flames.     

A field theoretical approach to the anomalous hall effect in semiconductors

The anomalous Hall effect for polarized electrons in semiconductors is calculated by a field theoretical method. The results obtained are essentially equivalent to those of Luttinger except for minor generalizations (the treatment of collisions is not limited to the first term in a Born expansion and the conductivity is calculated at finite frequency). The main purpose is to set a very simple formulation that can be used to treat more complicated problems, e.g. anomalous Hall effect in the presence of a magnetic field or with a resonant precessing spin magnetization. The existence of two distinct contributions to the anomalous Hall effect is clearly shown, one of which is missed in the transport equation formulation. The order of magnitude of each contribution is discussed for two different experimental situations.     

Dielectric properties of multiband electron systems I. Tight-binding formulation

The screened electron-electron interaction in a multi-band electron system is calculated within the random phase approximation and in the tight-binding representation. The obtained dielectric matrix contains, beside the usual site-site correlations, also the site-bond and bondbond correlations, and thus includes all physically relevant polarization processes. The arguments are given that the bond contributions are negligible in the long wavelength limit. We analyse the system with two non-overlapping bands in this limit, and show that the corresponding dielectric matrix reduces to a 2 × 2 form. The intra-band and inter-band contributions are represented by diagonal matrix elements, while the off-diagonal elements contain the mixing between them. The latter is absent in insulators but may be finite in conductors. Performing the multipole expansion of the bare long-range interaction, we show that this mixing is directly related to the symmetry of the atomic orbitals participating in the tight-binding electronic states. In systems with forbidden atomic dipolar transitions, the intra-band and inter-band polarizations are separated. However, when the dipolar transitions are allowed, the off-diagonal elements of the dielectric matrix are of the same order as diagonal ones, due to a finite monopole-dipole interaction between the intra-band and inter-band charge fluctuations. We also calculate the macroscopic dielectric function and obtain an expression which interpolates between the well-known limits of oneband conductors and pure insulators. In particular, it is shown that the microscopic origin of the so-called selfpolarization corrections is the on-site interaction which exchanges two electrons at different orbitals, combined with a finite tunneling between neighboring sites.     

Optical potential of a disordered array of scatterers

We study the propagation of scalar waves in a disordered array of static scatters. We derive a cluster expansion for the optical potential in analogy to that for the dielectric constant of a polarizable suspension. It is shown that the long range of the free space Green function leads to divergence of the cluster integrals at low energy. The divergences are removed by a resummation procedure analogous to the resummation of Mayer cluster integrals in the theory of electrolytes. We derive expressions for the most important contributions to the optical potential.     

The lattice dynamics of an anharmonic crystal

The theory of the physical properties of an anharmonic crystal is discussed by using the thermodynamic Green's functions for the phonons. A perturbation procedure is developed to obtain the Green's functions and it is shown that for some purposes a quasi-harmonic approximation is useful, in which the frequencies of the normal modes are those determined by infra-red or neutron spectrometry. The thermodynamic, elastic, dielectric and scattering properties of an anharmonic crystal are discussed in terms of the Green's functions, and detailed expressions are given for the more important contributions. Detailed numerical calculations are presented of the thermal expansion, dielectric properties and shapes of some of the inelastically scattered neutron groups, for sodium iodide and potassium bromide. The calculations, which give reasonable agreement with experiment, show that even at quite low temperatures, the lifetimes of some of the normal modes can be quite short. By using the quasi-harmonic approximation it is shown that the large temperature dependence of the normal modes in a ferroelectric crystal can be treated adequately.     

Electromagnetic momenta and forces in dispersive dielectric media

When the effects of dispersion are included, neither the Abraham nor the Minkowski expression for electromagnetic momentum in a dielectric medium gives the correct recoil momentum for absorbers or emitters of radiation. The total momentum density associated with a field in a dielectric medium has three contributions: (i) the Abraham momentum density of the field, (ii) the momentum density associated with the Abraham force, and (iii) a momentum density arising from the dispersive part of the response of the medium to the field, the latter having a form evidently first derived by Nelson (1991) [8]. All three contributions are required for momentum conservation in the recoil of an absorber or emitter in a dielectric medium. We consider the momentum exchanged and the force on a polarizable particle (e.g., an atom or a small dielectric sphere) in a host dielectric when a pulse of light is incident upon it, including the dispersion of the dielectric medium as well as a dispersive component in the response of the particle to the field. The force can be greatly increased in slow-light dielectric media.     

Scattering from axisymmetric obstacles embedded in axisymmetric dielectrics: The method of moments solution

The electromagnetic scattering from axisymmetric conducting or nonconducting (dielectric) obstacles, embedded in an axisymmetric dielectric body is treated. A surface integral equation formulation, consisting of coupled Fredholm equations of the first kind for the electric and magnetic fields, is solved by the method of moments. The outer surfaces of the internal obstacles and the embedding dielectrics can be nonconcentric, depart significantly from a spherical shape, but must be rotationally symmetric about a common axis. The embedding dielectric can be multilayered. Computer implementable expressions are given for the scattering cross sections for any desired polarization and for both backscatter (monostatic) and bistatic illumination. Comparisons are made with the extended boundary condition method for homogeneous dielectric bodies and the Mie theory extended for dielectrically clad conducting spheres. The generality of the present formulation is demonstrated for several other cladded scatterer configurations. This research was conducted under the McDonnell Douglas Independent Research and Development Program.     

1/N expansion and the correlation energy of nuclear matter in the relativistic σω model

We propose the 1/N expansion method, where N can be identified with 2 due to the isospin SU(2), as a systematic expansion scheme for the relativistic meson-nucleon many-body theory. We derive a general formula for the computation of the effective action in the σω model based on the 1/N expansion, utilizing the functional integral method. In this scheme the leading contribution coincides with the familiar Hartree approximation. The elimination of the Landau ghost from the meson propagators in the subgraphs, which appears to be essential for our formulation, is also established.

As an application we compute the energy density of nuclear matter beyond the Hartree approximation including the next-to-leading order contributions in the 1/N expansion. In this order, one should include the ring energy contribution as a correlation energy addition to the exchange energy contribution. We find that we can describe the nuclear matter saturation properties without drastic changes of the overall physical picture which emerged in the Hartree approximation. The important role of the repulsive contribution due to the vacuum polarization effects in the ring energy is emphasized.     

An FDTD method for the simulation of dispersive metallic structures

In this paper, we present a formulation of the finite-difference time-domain method for the simulation of metallic structures. The frequency dependent dielectric function of metals is approximated by a combined Drude–Lorentzian multi-pole expansion and fitting errors of only a few percent are obtained. An auxiliary differential equation technique is used to extend the standard FDTD algorithm with the dispersive material equations. The algorithm is validated by calculating reflection and transmission coefficients for thin metal layers, elliptical nano-particles and by simulating a surface plasmon resonance device. Excellent agreement between the FDTD simulations and exact theoretical results are obtained.     

Calculation and optimization of parameters of deep groove gratings with multilayer dielectric coating for compression of high-power laser pulses

The method of calculating the electromagnetic wave field diffracted by a holographic grating with a multilayer dielectric coating is developed. The method consists of the representation of the field inside dielectric layers in the form of a plane-wave expansion for weakly damped harmonics and an expansion over functions of the concomitant coordinate system for strongly damped orders. This modification of the method allows calculation of the diffraction efficiency and the electric field strength for the deep groove gratings. It is shown that a diffraction element that possess high efficiency and radiation strength can be obtained even when the profile of the dielectric layers flattens with an increase in the distance from the grating’s metallic layer.     

The magnetoelastic contribution to thermal expansion of rare-earth metal scheelites RLiF<Subscript>4</Subscript> (R = Tb-Yb)

The paper presents systematic experimental and theoretical studies of thermal expansion for rare-earth metal scheelites RLiF₄ (R = Tb-Ho, Tm, and Lu). Pronounced thermal expansion anomalies were observed. The magnetoelastic contributions were determined taking into account corrections for changes in the phonon contribution in the RLiF₄ series according to the Debye thermal expansion model. The calculated multipole moments of various orders for various rare-earth metal ions were compared to analyze the applicability of the quadrupole approximation to totally symmetric modes in the scheelite structure. For some ions (Ho and Tm), the magnetoelastic contributions to thermal expansion could not be described by the temperature dependences of their quadrupole moments, that is, multipole moments made considerable contributions. The totally symmetric magnetoelastic coefficients for the scheelite structure were determined from the experimental data on magnetoelastic contributions. These coefficients were compared with those for the zircon structure.     

Potential–density pairs for axisymmetric galaxies: the influence of scalar fields

We present a formulation for potential–density pairs to describe axi-symmetric galaxies in the Newtonian limit of scalar–tensor theories of gravity. The scalar field is described by a modified Helmholtz equation with a source that is coupled to the standard Poisson equation of Newtonian gravity. The net gravitational force is given by two contributions: the standard Newtonian potential plus a term stemming from massive scalar fields. General solutions have been found for axisymmetric systems and the multipole expansion of the Yukawa potential is given. In particular, we have computed potential–density pairs of galactic disks for an exponential profile and their rotation curves.     

Light propagation in nonuniform plasmonic subwavelength waveguide arrays

We study light propagation in nanoscale periodic structures composed of dielectric and metal in the visible range. We demonstrate that diffraction curves of nonuniform waveguide arrays can be tailored by varying the geometric and dielectric features of the waveguides. The results obtained from a proper formulation of coupled mode theory for nonuniform arrays are validated through numerical solution of Maxwell equations in frequency domain.     

Scattering of a Plane Electromagnetic Wave by an Infinite Dihedral Wedge with a Slotted Cylinder at the Apex

The problem of scattering of a plane electromagnetic wave by a perfectly conducting dihedral wedge with a slotted cylinder at the apex in rigorous formulation is reduced to solving a system of linear algebraic equations for unknown coefficients of the Fourier expansion of the scattered field. The results of calculation of the far-zone field with a given accuracy are presented in the case of an E-polarized incident wave. It is shown that for a slot with a large opening angle, the radiation patterns of the field in the long-wavelength far zone has a shape similar to a cardioid and does not depend on the incident-wave direction and the dielectric permittivity of the cylinder. In the case of a narrow slot, the radiation-pattern shape depends significantly on the incidence angle of the wave.     

Second virial coefficients for a fluid of dipolar hard ellipsoids

We calculate the two body contributions to the pressure, dielectric constant, depolarized light scattering intensity, electro-optical birefringence (Kerr effect), and other properties, of a fluid whose molecules are hard ellipsoids with embedded central point dipoles. The results are presented for various molecular anisotropies and dipole strengths. The second dielectric and Kerr virial coefficients are found to be particularly sensitive to molecular shape.     

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ?(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ? as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.     

空气环型二维光子晶体完全带隙特性研究

采用平面波展开法, 系统研究了空气环型二维光子晶体的完全光子带隙随结构参数变化而改变的规律, 并将其与普通的空气孔型和介质柱型二维光子晶体的完全带隙进行了比较. 研究表明: 空气环型二维光子晶体不仅可以获得更宽的完全带隙, 而且, 当介质折射率较低时, 其可以获得普通空气孔型和介质柱型二维光子晶体在低折射率条件下所无法获得的完全带隙. 关键词： 空气环型二维光子晶体 完全带隙 平面波展开法