Static Point Charge Research Articles

Exact multicentered static point charge source distributions in the Born–Infeld theory of nonlinear electromagnetism and presence of electric and magnetic currents

Exact multicentered solutions to the governing equations of the Born–Infeld nonlinear theory of electrodynamics describing distributions of electric, magnetic, and dyonic point charge sources are constructed explicitly for the first time. The method of construction may effectively be adapted to obtain such solutions in generalized theories as well. As a consequence, the solutions unveil that, in order to achieve a balance between such multicentered electric or magnetic point charge distribution in equilibrium, a static magnetic or electric current must be present, resulting in non-conservativeness of the induced electric or magnetic intensity field, respectively and universally. Moreover, it is also shown that the methods of construction and conclusions drawn in the multicentered situation may be extended to obtain exact solutions and similar conclusions, explicitly, in the situation of continuously distributed charge source problems.

A Full Quantum Mechanical Approach Assessing the Chemical and Electromagnetic Effect in TERS.

Tip-enhanced Raman spectroscopy (TERS) is a valuable method for surface analysis with nanometer to angstrom-scale resolution; however, the accurate simulation of particular TERS signals remains a computational challenge. We approach this challenge by combining the two main contributors to plasmon-enhanced Raman spectroscopy and to the high resolution in TERS, in particular, the electromagnetic and the chemical effect, into one quantum mechanical simulation. The electromagnetic effect describes the sample's interaction with the strong, highly localized, and inhomogeneous electric fields associated with the plasmonic tip and is typically the thematic focus for most mechanistic studies. On the other hand, the chemical effect covers the different responses to the extremely close-range and highly position-sensitive chemical interaction between the apex tip atom(s) and the sample, and, as we could show in previous works, plays an often underestimated role. Starting from a (time-dependent) density functional theory description of the chemical model system, comprised of a tin(II) phthalocyanine sample molecule and a single silver atom as the tip, we introduce the electromagnetic effect through a series of static point charges that recreate the electric field in the vicinity of the plasmonic Ag nanoparticle. By scanning the tip over the molecule along a 3D grid, we can investigate the system's Raman response on each position for nonresonant and resonant illumination. Simulating both effects on their own already hints at the achievable signal enhancement and resolution, but the combination of both creates even stronger evidence that TERS is capable of resolving submolecular features.

Point particles and Appell’s solutions on the axis of a Kerr black hole for an arbitrary spin in terms of the Debye potentials

The Teukolsky master equation -- a fundamental equation for test fields of any spin, or perturbations, in type D spacetimes -- is classically treated in its separated form. Then the solutions representing even the simplest sources -- point particles -- are expressed in terms of series. The only known exception is a static particle (charge or mass) in the vicinity of Schwarzschild black hole. Here, we present a generalization of this result to a static point particle of arbitrary spin at the axis of Kerr black hole. A simple algebraic formula for the Debye potential from which all the NP components of the field under consideration can be generated is written down explicitly. Later, we focus on the electromagnetic field and employ the classic Appell's trick (moving the source into a complex space) to get so called electromagnetic magic field on the Kerr background. Thus the field of nontrivial extended yet spatially bounded source is obtained. We also show that a static electric point charge above the Kerr black hole induces, except an expected electric monopole, also a magnetic monopole charge on the black hole itself. This contribution has to be compensated. On a general level we discuss Teukolsky-Starobinsky identities in terms of the Debye potentials.

Electrostatic Potential Optimized Molecular Models for Molecular Simulations: CO, CO2, COS, H2S, N2, N2O, and SO2.

Molecular simulations have been widely employed in the discovery of nanoporous materials, such as metal-organic frameworks (MOFs) and zeolite, for energy- and environment-related applications. To achieve simulation predictions with better accuracy, we herein present a collection of molecular models, including carbon monoxide (CO), carbon dioxide (CO2), carbonyl sulfide (COS), hydrogen sulfide (H2S), nitrogen (N2), nitrous oxide (N2O), and sulfur dioxide (SO2). These models, denoted as electrostatic potential optimized molecular models (ESP-MMs), are systematically developed to not only reproduce experimental vapor-liquid equilibrium but also have accurate electrostatic potential representation surrounding the molecules. Our results show that, with accurate electrostatic potential representations, ESP-MMs can offer improved predictions in a variety of adsorption properties for porous materials, including MOFs with open-metal sites and all-silica zeolites. Specifically, by using ESP-MMs, the binding geometry and adsorption energy landscape can be well captured. This enables these models to be employed to unravel the fundamental mechanism of gaseous adsorption in materials of interest as well as to facilitate the parametrization of adsorbent-adsorbate interactions. We also demonstrate that, combined with generic force fields for adsorbents, ESP-MMs can offer reasonable predictions in adsorption isotherms. Although these ESP-MMs use a relatively simple and nonpolarizable potential form for the sake of efficiency and applicability, their accuracy has been extensively validated in this study. Furthermore, the set of Lennard-Jones potentials with static point charges adopted for ESP-MMs can be readily implemented in all available simulation packages. We anticipate that these ESP-MMs can largely facilitate future computational studies of porous materials for gas separation and removal.

EF-Index: Determining number of clusters (K) to estimate number of segments (S) in an image

Estimation of number of segments in an image attracts a formidable interest among the research community. The number of segments in an image is estimated by calculating the number of clusters present in the pixels of that image. The present work offers an unsupervised method, named “Electrostatic Force Index (EF-Index)”, to estimate the number of clusters inherent in an image, reporting of which is very rare in literature. The proposed approach is inspired by Coulomb's law of electrostatics. The EF-Index explores the mutual influence of an arbitrary pixel on another, by considering them similar to point charges. Our proposed cluster indexing method, viz. EF-Index is capable of determining the number of clusters present in an image. It has a strong resemblance to the way the electrostatic force is operative between a pair of static point charges in a closed system as per Coulomb's principle. In order to justify the effectiveness of the proposed approach, we have compared EF-Index of a given image with DB-Index, I-Index, CVNN-Index, DOE-AND-SCA and Sym-Index of the same image. Experimental results show that EF-Index is same as other state-of-the-art indices, whereas EF-Index does not require any clustering algorithm. To establish the applicability of the EF-Index, the same is applied for image segmentation considering Berkeley Segmentation Dataset and Stanford Background Dataset. We observe the results obtained conform to the ground truth and results achieved by applying existing well-established segmentation techniques on the same datasets. The efficacy of the proposed approach is further substantiated in terms of its reduced computational overhead in comparison to the state-of-the-art segmentation algorithms.

Arbitrarily coupled massive scalar field in conical thin-shell spacetimes

We study the massive scalar field of a charged particle held at rest in conical thin-shell spacetimes with one or two asymptotic regions. Resonant and stable scalar Green’s functions are characterized in terms of the coupling of the field to the trace of the extrinsic curvature jump at the shell. Stable coupling values, within the safety domain of the configuration parameters, are used to analyze the self-force of static point charges.

Dynamical Rashba Band Splitting in Hybrid Perovskites Modeled by Local Electric Fields

We report a computational method for evaluating the dynamical Rashba interaction coefficient of tetragonal and cubic methylammonium lead iodide (MAPbI3) perovskite, at various size scales, through Car–Parrinello molecular dynamics trajectories. This strategy involves the calculation of a time-dependent band structure of the target systems using periodic boundary conditions and the evaluation of the amplitude of band-splitting due to the spin–orbit coupling (SOC) with the computation of a local electric field. This model, physically motivated by a rewriting of the SOC Hamiltonian according to the heterogeneity of three-dimensional systems and our choice of k-space sampling, involves directly the methylammonium configuration space sampling. Originally applied to tetragonal and cubic unit cells with static point-charges, this model is further ameliorated in order to take into account the replication of this unit cell through space and to account for the dynamical nature of charge distribution. Once our proto...

Leading the non-cancelling IR divergences in massless gauge theories: Abelian case

We study the cancellation of both soft and collinear infrared divergences at next-to-leading order correction in a process where a massless electron is scattered off of a static point charge. We show that a self-consistent application of the KLN theorem requires including all initial and final degenerate states, which require including diagrams with an arbitrary number of disconnected photons forming a divergent series. We improve on previous work by rearranging the series in a controlled way and exploit the Monotone Convergence Theorem to prove the uniqueness of our rearranged result. This rearrangement yields a factorization of the infinite contribution from the initial state soft photons, that then cancels in the physically observable cross section.

Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States.

We present for the first time a quantum mechanics/molecular mechanics scheme which combines quantum Monte Carlo with the reaction field of classical polarizable dipoles (QMC/MMpol). In our approach, the optimal dipoles are self-consistently generated at the variational Monte Carlo level and then used to include environmental effects in diffusion Monte Carlo. We investigate the performance of this hybrid model in describing the vertical excitation energies of prototypical small molecules solvated in water, namely, methylenecyclopropene and s-trans acrolein. Two polarization regimes are explored where either the dipoles are optimized with respect to the ground-state solute density (polGS) or different sets of dipoles are separately brought to equilibrium with the states involved in the electronic transition (polSS). By comparing with reference supermolecular calculations where both solute and solvent are treated quantum mechanically, we find that the inclusion of the response of the environment to the excitation of the solute leads to superior results than the use of a frozen environment (point charges or polGS), in particular, when the solute-solvent coupling is dominated by electrostatic effects which are well recovered in the polSS condition. QMC/MMpol represents therefore a robust scheme to treat important environmental effects beyond static point charges, combining the accuracy of QMC with the simplicity of a classical approach.

A novel quantum-mechanical interpretation of the Dirac equation

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr–Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit , where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie–Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born–Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

Static self-forces in a five-dimensional black hole spacetime

We obtain the electric field and scalar field for a static point charge in closed form in the 5D Schwarzschild-Tangherlini black hole spacetime. We then compute the static self-force in each of these cases by assuming that the appropriate singular field is a 4D Hadamard Green's function on the constant time Riemannian slice. It is well known that the Hadamard Green's function involves an arbitrary regular biscalar $W_{0}(x,x')$, whose coincidence limit $w(x)$ appears in the expression for the self-force. We develop an axiomatic approach to reduce this arbitrary function to a single arbitrary dimensionless coefficient. We show that in the context of this approach to regularization, the self-force does not depend on any undetermined length-scale and need not depend on the internal structure of the charge.

Chromophore-protein coupling beyond nonpolarizable models: understanding absorption in green fluorescent protein.

The nature of the coupling of the photoexcited chromophore with the environment in a prototypical system like green fluorescent protein (GFP) is to date not understood, and its description still defies state-of-the-art multiscale approaches. To identify which theoretical framework of the chromophore-protein complex can realistically capture its essence, we employ here a variety of electronic-structure methods, namely, time-dependent density functional theory (TD-DFT), multireference perturbation theory (NEVPT2 and CASPT2), and quantum Monte Carlo (QMC) in combination with static point charges (QM/MM), DFT embedding (QM/DFT), and classical polarizable embedding through induced dipoles (QM/MMpol). Since structural modifications can significantly affect the photophysics of GFP, we also account for thermal fluctuations through extensive molecular dynamics simulations. We find that a treatment of the protein through static point charges leads to significantly blue-shifted excitation energies and that including thermal fluctuations does not cure the coarseness of the MM description. While TDDFT calculations on large cluster models indicate the need of a responsive protein, this response is not simply electrostatic: An improved description of the protein in the ground state or in response to the excitation of the chromophore via ground-state or state-specific DFT and MMpol embedding does not significantly modify the results obtained with static point charges. Through the use of QM/MMpol in a linear response formulation, a different picture in fact emerges in which the main environment response to the chromophore excitation is the one coupling the transition density and the corresponding induced dipoles. Such interaction leads to significant red-shifts and a satisfactory agreement with full QM cluster calculations at the same level of theory. Our findings demonstrate that, ultimately, faithfully capturing the effects of the environment in GFP requires a quantum treatment of large photoexcited regions but that a QM/classical model can be a useful approximation when extended beyond the electrostatic-only formulation.

Interaction of a magnet and a point charge: Unrecognized internal electromagnetic momentum

Whereas nonrelativistic mechanics always connects the total momentum of a system to the motion of the center of mass, relativistic systems, such as interacting electromagnetic charges, can have internal linear momentum in the absence of motion of the system's center of energy. This internal linear momentum of a system is related to the controversial concept of “hidden momentum.” We suggest that the term “hidden momentum” be abandoned. Here, we use the relativistic conservation law for the center of energy to give an unambiguous definition of the “internal momentum of a system,” and then we exhibit this internal momentum for the system of a magnet (modeled as a circular ring of moving charges) and a distant static point charge. The calculations provide clear illustrations of this system for three cases: (a) the moving charges of the magnet are assumed to continue in their unperturbed motion; (b) the moving charges of the magnet are free to accelerate but have no mutual interactions; and (c) the moving charges of the magnet are free to accelerate and also interact with each other. When the current-carrying charges of the magnet are allowed to interact, the magnet itself will contain internal electromagnetic linear momentum, something that has not been described clearly in the research and teaching literature.

Strictly Finite Range Forces from the Signum-Gordon Field: Exact Results in two Spatial Dimensions

Exact formula for the force between two identical static point charges coupled to the nonlinear scalar field of two-dimensional signum-Gordon model is obtained. Pertinent solution of the field equation is found in the form of one-dimensional integral. The force exactly vanishes when the distance between the charges exceeds certain critical value.

Semiconductor nanotube plasma

The theory of dispersion of surface plasma waves in semiconductor nanotubes is presented. The effect of screening the Coulomb field of a static point charge by a magnetized electron gas of a nanotube is investigated. The main properties of the semiconductor nanotube plasma, 3D plasma, and planar 2D plasma are compared. The dependences of the critical temperature and thermodynamic properties of a superconducting quantum cylinder on the characteristics of the system are studied.

Electrostatics in the Surroundings of a Topologically Charged Black Hole in the Brane

We determine the expression for the electrostatic potential generated by a point charge held stationary in the topologically charged black hole spacetime arising from the Randall-Sundrum II braneworld model. We treat the static electric point charge as a linear perturbation on the black hole background and an expression for the electrostatic multipole solution is given: PACS: 04.70.-s, 04.50.Gh, 11.25.-w, 41.20.-q, 41.90.+e.

Probing global aspects of a geometry by the self-force on a charge: Spherical thin-shell wormholes

The self-interaction for a static point charge in the space-time of a thin-shell wormhole constructed connecting two identical Schwarzschild geometries is calculated in a series expansion. The electrostatic self-force is evaluated numerically. It is found to be attractive towards the throat except for some values of the throat radius proximate to the value of the Schwarzschild horizon for which the force is repulsive or attractive depending on the position of the charge. The result differs from the self-force in the space-time of the Schwarzschild black hole, where it is always repulsive from the center. Although these wormhole and black hole geometries are locally indistinguishable, the different topologies of both backgrounds are manifested in the electrostatic field of a point charge.

Electrostatic potential of a point charge in a Brans-Dicke Reissner-Nordström field

We consider the Brans-Dicke Reissner-Nordstrom spacetime in isotropic coordinates and the electrostatic field of an electric point charge placed outside its surface of inversion. We treat the static electric point charge as a linear perturbation on the Brans-Dicke Reissner-Nordstrom background. We develop a method based upon the Copson method to convert the governing Maxwell equation on the electrostatic potential generated by the static electric point charge into a solvable linear second order ordinary differential equation. We obtain a closed form fundamental solution of the curved space Laplace equation arising from the background metric, which is shown to be regular everywhere except at the point charge and its image point inside the surface of inversion. We also develop a method that demonstrates that the solution does not contain any other charge that may creep into the region that lies beyond the surface of inversion and which is not covered by the isotropic coordinates. The Brans-Dicke Reissner-Nordstrom spacetime therefore is linearly stable under electrostatic perturbations. This stability result includes the three degenerate cases of the fundamental solution that correspond to the Brans Type 1, the Reissner-Nordstrom and the Schwarzschild background spacetimes.

Electronic Ferroelectricity in a Molecular Crystal with Large Polarization Directing Antiparallel to Ionic Displacement

Ferroelectric polarization of 6.3 μC cm(-2) is induced by the neutral-to-ionic transition, upon which nonpolar molecules of electron donor tetrathiafulvalene (TTF) and acceptor p-chloranil (CA) are incompletely ionized to ±0.60e and dimerized along the molecular stacking chain. We find that the ferroelectric properties are governed by intermolecular charge transfer rather than simple displacement of static point charge on molecules. The observed polarization and poling effect on the absolute structural configuration can be interpreted in terms of electronic ferroelectricity, which not only exhibits antiparallel polarity to the ionic displacement but also enhances the polarization more than 20 times that of the point-charge model.

Are single C60 fullerenes dielectric or metallic?

We present analytical solutions for the interaction energies between a static point charge and a metal- or a dielectric sphere. These solutions include polarization effects to infinite orders in the inverse of the distance between the point charge and the spheres. Further, we present Density Functional Theory (DFT) calculations of interaction energies for a point charge in ranges of fixed positions outside a neutral or a singly charged C(60) molecule. Based on these DFT results, we conclude that the metal sphere model describes the electronic response of the C(60) molecule much better than the dielectric sphere model. These findings are particularly important for calculations of energy barriers for charge transfer in reactions involving C(60) molecules. The metal- and dielectric models should further be useful for descriptions of, for example, the polarizabilities of and interactions with conducting and insulating spherical clusters or particles.