Static Point Charge Research Articles

Dynamic creation of electrostatic fields

To illustrate the concept of the dynamic creation of static fields, the fields associated with the creation of a static point charge and a static point dipole between times t=0 and t=τ are calculated. For the former the field is that of a static charge in all space once t>τ. For the static point dipole the field pattern consists of three zones once t>τ: An expanding sphere of radius r=c(t−τ) in which the field is that of a static dipole, a shell defined by c(t−τ)<r<ct, containing both electric and magnetic intermediate and far field components, and the volume beyond the event horizon, r>ct, for which the fields vanish. Despite the fact that the electric field occupies an increasing volume in space with increasing time, the energy in the field is constant once the dipole has been created. This result is established explicitly for an arbitrary creation of the static dipole.

Finding fields and self-force in a gauge appropriate to separable wave equations

Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a ``radiation gauge.'' The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component ${\ensuremath{\psi}}_{0}$ (or ${\ensuremath{\psi}}_{4}$) of the Weyl tensor and follows earlier work by Chrzanowski, Cohen, and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but ${\ensuremath{\psi}}_{0}$ and ${\ensuremath{\psi}}_{4}$ are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin $\ifmmode\pm\else\textpm\fi{}2$ parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the Detweiler-Whiting construction of the singular field. It relies on the fact that the renormalized ${\ensuremath{\psi}}_{0}$ (or ${\ensuremath{\psi}}_{4}$) is a source-free solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.

Quantization and simulation of Born-Infeld nonlinear electrodynamics on a lattice

Born-Infeld non-linear electrodynamics arises naturally as a field theory description of the dynamics of strings and branes. Most analyses of this theory have been limited to studying it as a classical field theory. We quantize this theory on a Euclidean 4-dimensional space-time lattice and determine its properties using Monte-Carlo simulations. The electromagnetic field around a static point charge is measured using Luscher-Weisz methods to overcome the sign problem associated with the introduction of this charge. The D field appears identical to that of Maxwell QED. However, the E field is enhanced by quantum fluctuations, while still showing the short distance screening observed in the classical theory. In addition, whereas for the classical theory, the screening increases without bound as the non-linearity increases, the quantum theory approaches a limiting conformal field theory.

Nonlinear screening and stopping power in two-dimensional electron gases

We have used density-functional theory to study the nonlinear screening properties of a two-dimensional (2D) electron gas. In particular, we consider the screening of an external static point charge of magnitude $Z$ as a function of the distance of the charge from the plane of the gas. The self-consistent screening potentials are then used to determine the 2D stopping power in the low-velocity limit based on the momentum transfer cross section. Calculations as a function of $Z$ establish the limits of validity of linear and quadratic response theory calculations, and show that nonlinear screening theory already provides significant corrections in the case of protons. In contrast to the 3D situation, we find that the nonlinearly screened potential supports a bound state even in the high-density limit. This behavior is elucidated with the derivation of a high-density screening theorem which proves that the screening charge can be calculated perturbatively in the high-density limit for arbitrary dimensions. However, the theorem has particularly interesting implications in 2D where, contrary to expectations, we find that perturbation theory remains valid even when the perturbing potential supports bound states.

Electrostatic Theory for Pseudochiral Omega and Transversal Chiral Media

The problem of unbounded pseudochiral omega media and transversal chiral media in the presence of both static electric and magnetic point charges is studied. The scalar electric and magnetic potentials in these media are introduced. Using these potentials, the associated electric and magnetic fields are determined. The problem of static electric and magnetic current sources as well as the electromagnetic fields is carried out. It is observed that for pseudochiral omega media, there is cross coupling between electric and magnetic fields in the case of current sources. But there is not any cross coupling in the case of point charges. For transversal chiral media, in both cases (current sources, point charges), the magneto-electric cross coupling exists through chirality parameter of the medium.

Comparison of electrostatic potential around proteins calculated from Amber and AM1 charges: application to mutants of prion protein

On the basis of arguments of complementary fit of shape and charge polarity or hydrophobicity, molecular electrostatic potentials (MEPs) around proteins are commonly used to deduce likely sites for interaction with ligands or other proteins, including for variations such as mutations. But protein MEPs calculated classically from fixed force field descriptions, including those with implicit solvent models such as in Delphi, do not allow for repolarization of protein residues within the protein system; hence, their representations are likely to be variably inaccurate. Linear-scaling methods now allow calculation of MEPs quantum mechanically for systems as large as proteins, and can account for polarization explicitly. Here we compare MEPs derived from AM1 charge distributions calculated by Mopac2000 with those from the classical Amber force field. Our models are mutants of prion protein (PrP), a protein with an unusually high number of charged residues. The results demonstrate that static point charges, as used in most current force fields, cannot reproduce the MEP of macromolecules. Also, it is not sufficient to account for the influence of nearby atoms connected by chemical bonds; the influence of nearby atoms in space is at least as important. Thus, further progress in the accuracy and wider applicability of force fields requires proper accounting for polarization. Mopac2000 calculations can provide the necessary data for checking new force fields and/or parameter fitting.

THE THEORY OF UNIAXIAL BI-ANISOTROPIC MEDIA: THE QUASI-STATIC CASE

The problem of unbounded uniaxial bi-anisotropic media in the presence of both static electric and magnetic point charges is investigated. For this purpose scalar electric and magnetic potentials in these media are introduced. Using these potentials, the corresponding electric and magnetic fields are then determined. The similar problem of static electric and magnetic current sources with the goal of finding the electromagnetic fields is carried out. It is observed that either of static electric or magnetic point charge produces both electric and magnetic fields. Furthermore, it is observed that only the transverse components of current sources with respect to axis of the medium produce the axial field components.

Electronic structure properties of solvated biomolecules: A quantum approach for macromolecular characterization

Linear-scaling electronic structure calculations of solvated biomolecules have been carried out using a semiempirical Hamiltonian and a new smooth solvation potential. These methods afford a new way of generating macromolecular properties that include quantum electronic structure. In addition to the widely used classical electrostatic potential maps based on empirically derived static point charges, now fully quantum mechanical electrostatic potentials that include electronic polarization are possible. Linear-scaling electronic structure methods provide a host of response properties of the electron density such as linear response functions, local hardness functions, and Fukui functions. It is the hope that these indices will extend insight into problems of biological macromolecular characterization. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1562–1571, 2000

A chemical potential equalization method for molecular simulations

A formulation of the chemical potential (electronegativity) equalization principle is presented from the perspective of density-functional theory. The resulting equations provide a linear-response framework for describing the redistribution of electrons upon perturbation by an applied field. The method has two main advantages over existing electronegativity equalization and charge equilibration methods that allow extension to accurate molecular dynamics simulations. Firstly, the expansion of the energy is taken about the molecular ground state instead of the neutral atom ground states; hence, in the absence of an external field, the molecular charge distribution can be represented by static point charges and dipoles obtained from fitting to high-level ab initio calculations without modification. Secondly, in the presence of applied fields or interactions with other molecules, the density response can be modeled accurately using basis functions. Inclusion of basis functions with dipolar or higher order multipolar character allows molecules or chemical groups to have correct local anisotropic polarizabilities. A modified semiempirical form of the hardness matrix has been introduced that can be evaluated efficiently using Gaussians, and requires only one parameter per basis function. Applications at two basis-set levels demonstrate the method can accurately reproduce induced dipole moments and estimated chemical potentials obtained from density-functional calculations for a variety of molecules. Inclusion of basis functions beyond the conventional spherical-atom type is essential in some instances. The present formulation provides the foundation for a promising semi-empirical model for polarization and charge transfer in molecular simulations.

Optimization of centroid-finding algorithms for cathode strip chambers

We compare the data obtained by a precision cathode strip chamber (CSC) with a static point charge model. The observed strip charge profile is in good agreement with the model prediction. We have used this model to calculate the systematic error of some popular centroid-finding algorithms, and found good agreement with the systematic error observed in the data. We further studied the effect of incidence angle and of anode wire displacements. By using an algorithm based on a hyperbolic secant function (sech 2) to describe the charge profile, we are able to improve the published single layer resolution of our CSC prototype in a muon beam by 14%, from 53.3 ± 0.9 to 45.8 ± 0.7μm.

Interaction of coupled plasmon-phonon modes with a point charge in a polar semiconductor

The coupled plasmon--longitudinal-optical-phonon modes of a degenerate inhomogeneous electron or hole gas in a bulk compound semiconductor are studied. The interaction of a point charge with these coupled modes is derived in the random-phase approximation for both the carriers and the phonons in a form which is appropriate for treating inhomogeneous carrier systems. An integral equation governing the interaction of a static point charge with these coupled modes is derived which has the same form as that in the case of a point-charge interacting with plasmons alone but in which the parameters are modified by the coupling to phonons. As a specific example, these results are used to study the binding of the coupled plasmon-phonon modes to point charges in degenerate compound semiconductors, and it is found that such bound states will exist only at very low carrier densities.

Quasi-static image theory for the bi-isotropic sphere

Image theory for the static point charge and the conducting sphere, produced by Kelvin's inversion theory, is extended to the bi-isotropic sphere, including the chiral sphere as a special case. Image expressions for the bi-isotropic sphere can be derived in a manner similar to that of the dielectric sphere except that the quasi-static problem now involves both electric and magnetic scalar potentials, coupled through the interface conditions at the spherical surface. The image is a combination of electric and magnetic line charges along the axis connecting the point charge and the center of the sphere, and their expressions are obtained through what can be labeled as finite Mellin transformation. The expressions derived can find application in more complete quasi-static analyses of interactions of bi-isotropic spherical particles in artificial bi-isotropic media. >

Dependence of surface screening in semiconductors on the short-range properties of the bulk dielectric function

Abstract We calculate the induced potential due to a static point charge near a semiconductor surface including the proper short-range behavior of the bulk dielectric function within an analytical scheme previously developed. It is found that the image potential is not appreciably affected by this inclusion up to about 1 a.u. from the surface.

The anisotropic ligand polarization intensity mechanism in dihedral lanthanide(III) complexes

The f-f electronic spectra of a D 4 coordination compound [Eu(III)(2,2′-bipyridine-N,N′-dioxide)4]3+ and of D 3 analogues indicate, on comparison, that only the ΔMJ = ±1 component of the quadrupolar Eu(III) 7 F 0 → 5 D 2 transition is active in the D 4 case. The intensity of a quadrupolar metal-ion transition in a D 4 complex is governed uniquely by a single rank-2 environmental ligand tensor, within the restriction to one-electron operators, and it generates a first order electric dipole moment solely for the ΔMJ = ± 1 transition component. A rank-2 ligand tensor cannot arise from a configurational interaction mechanism based upon a static point-charge or dipolar crystal field, nor from the dynamic ligand-polarization mechanism in the mean polarizability approximation. The extension of the latter mechanism to include the polarizability anisotropy of the ligand bonds gives a rank-2 ligand polarization field tensor F (2) 0 which accounts for the 7 F 0 → 5 D 2 dipole strength of the D 4 complex investigated.

Classical models of confinement II

We generalize the class of Abelian models of paper I which lead to a linear potential between opposite charges. The electric fieldE is here taken as a power series in the electric displacementD raised to the σth power. We solve to first order the case of two opposite static point charges asymptotically for large separations.

Classical models of confinement

We investigate the structure of classical models of confinement by analytic methods. The models considered involve just one abelian gauge field and can be viewed as non-linear versions of Maxwell's theory. We study in detail the case of two opposite static point charges. A scaling law is found for small separations of the charges, while a perturbation treatment is developed for large separations. The results obtained for large separations include an exact evaluation of the first correction term to the linear potential and a classification of the asymptotic field configurations.

RPA response to a static point charge near a metal surface: Finite-barrier treatment

RPA response to a static point charge near a metal surface: Finite-barrier treatment

Response of a semi-infinite cubic lattice to a static point charge

The interaction energy of a point charge external to a semi-infinite cubic lattice is calculated from the self-consistent solution for the driven atomic dipoles. The static local fields are calculated for a lattice of polarizable nonpolar point atoms. The energy is expressed as a power series in the atomic polarizability; analytical and numerical results for the first two coefficients in the series are given over a wide range of charge-lattice separations. A modified continuum electrostatic-image energy is remarkably accurate for charge-lattice separations down to one lattice spacing.

Renormalization theory of charged particles in an insulator and the effective-mass approximation

The problem of charged particles added to a perfect insulator is analysed with the use of time-independent many-electron perturbation theory. It is shown that all added particles, both classical (static point charges) and quantum (electrons and holes), interact via a screened coulomb potential provided the particles are sufficiently far apart. This screening may be regarded as renormalization of the charges according to the intuitively appealing prescription q ->qk-1/2, where k is interpreted as the static dielectric constant, as originally conjectured by Kohn. When dynamical particles are involved the results establish the general validity of the well-known effective-mass equation which describes the motion of the quasiparticles and hence equivalently, the low-lying excitations of the whole many-electron system.

Response of Metal Surfaces to Static and Moving Point Charges and to Polarizable Charge Distributions

A phenomenological dielectric approximation is proposed for studying the response of metal surfaces to external charge distributions and is illustrated by detailed calculations using the Thomas-Fermi model. The procedure is based on the replacement of the dielectric-response kernel in a constitutive relation by its asymptotic expression in the bulk region. It represents an alternative to the classical step-density approximation, where the nonuniform density profile near the surface is replaced by the bulk electron density up to an abrupt termination. While the two procedures are equivalent for a local solid, they are quite different in general because of the different nature of the quantitites being approximated by bulk expressions. Detailed applications include the calculation of the image-potential interaction and of the induced surface dipole for static point charges external to the metal surface, the study of the corresponding quantities for charges embedded in the surface, and, finally, the calculation of the effective polarizability of an adsorbed atom and of the image potential and induced surface dipole for a polarizable ion. Comparison with self-consistent surface-model calculations indicates that for charges external to the surface the results for the above-mentioned dielectric approximation are much more realistic than those for the step-density approximation. However, for the case of embedded charges far away from the surface the step-density approximation yields a more accurate result for the surface dipole. A final section is devoted to the generalization of the step-density treatment to time-dependent response problems, assuming specular reflection of electrons at the surface. Some necessary general formulas are derived in a first part, which is then followed by a detailed study of the image-potential interaction for point charges moving uniformly along various prescribed trajectories. Explicit calculations for a local dielectric function indicate a strong dependence of the instantaneous interaction on the past trajectory of the external charge, as well as strong deviations from the quasistatic image potential in some cases. These modifications arise from real and virtual excitation of surface plasmons for particles moving outside the metal, and from both surface- and bulk-plasmon excitation for particles moving inside the metal.