Long-range Asymptotics Research Articles

A note on the electrical potential distribution around a test charge in anisotropic collisional plasmas

AbstractIn this paper, we discuss recent results concerning the electrical potential distribution around a small test charged particle in weakly ionized collisional plasmas in the presence of an ion flow. The effect of plasma absorption on the particle surface is taken into account and the results are compared with those from earlier models neglecting absorption. In the considered regime, the effect of plasma absorption is quite important and completely determines the long-range asymptote of the electrical potential.

Attraction of Positively Charged Particles in Highly Collisional Plasmas

It is shown that the electrostatic interaction potential between a pair of positively charged particles embedded in a highly collisional plasma has a long-range attractive asymptote. The effect is due to continuous plasma absorption on the particles. The relevance of this result to experimental investigations of complex (dusty) plasmas is discussed.

Long-range asymptotics of a step signal propagating in a hereditary viscoelastic medium

The shape of the asymptotic long-range solution of the scalar linear viscoelastic signaling problem is found for a large class of creep compliances. If the asymptotic growth of the creep compliance at large times is given by a power law then the long-range asymptotic shape of an initial step pulse is given by a function depending exclusively on the value of the exponent in the power law. Two different cases arise corresponding to unbounded and bounded creep compliances. In the first case the asymptotic solution is the solution of a fractional wave equation with a scale factor. In the second case a different universal signal shape function is obtained.

Electrostatic potential behind a macroparticle in a drifting collisional plasma: Effect of plasma absorption

The electric field and potential behind a small absorbing body (dust grain) at floating potential has been calculated analytically in a highly collisional drifting plasma. Linear plasma response formalism has been used and main attention has been focused on the effect of plasma absorption on the grain. It is shown that the long-range asymptote of the electric field is dominated by the effect of absorption and is always negative. Depending on plasma parameters, the electric field at intermediate distances can either increase monotonically or exhibit one maximum and one minimum. It can achieve positive values in certain parameter regimes, which indicates the possibility of electrostatic attraction between the grains aligned parallel to the flow. The obtained results can be important for understanding of the binary grain interactions in complex plasmas at elevated pressures.

Macroparticle screening in a weakly ionized plasma

Kyiv National Taras Shevchenko University, Kyiv, Ukraine(Received 29 January, 2007)A new approach is proposed for the analytical description of e˙ective grain potentials in dustyplasmas. The basic idea is to describe absorption of electrons and ions bythe macroparticle in termsof e˙ective point sinks introduced into the equations of plasma dynamics. The proposed approachmakes it possible to ˝nd explicit relations for the potential and particle densities distributions nearthe grain. It is shown that plasma particle absorption results in the long-range asymptotics of thee˙ective grain potentials. The dynamical screening of the moving dust particle is considered as well.The energy of the grain interaction with the induced charge produced by the grain and the forceacting on the moving dust particle are calculated. The possibility of negative friction for the movinggrain is shown.Key words: dusty plasma, e˙ective potential, charge screenjng.PACS number(s): 52.27.LwI. INTRODUCTION

Electric forces induced by a charged colloid particle attached to the water–nonpolar fluid interface

Here, we solve the problem about the electric field of a charged dielectric particle, which is adsorbed at the water–nonpolar fluid (oil, air) boundary. The solution of this problem is a necessary step for the theoretical prediction of the electrodipping force acting on such particle, as well as of the electrostatic repulsion and capillary attraction between two adsorbed particles. In accordance with the experimental observations, we consider the important case when the surface charges are located at the particle–nonpolar fluid boundary. To solve the electrostatic problem, the Mehler–Fock integral transform is applied. In the special case when the dielectric constants of the particle and the nonpolar fluid are equal, the solution is obtained in a closed analytical form. In the general case of different dielectric constants, the problem is reduced to the numerical solution of an integral equation, which is carried out by iterations. The long-range asymptotics of the solution indicates that two similar particles repel each other as dipoles, whose dipole moments are related to the particle radius, contact angle, dielectric constant and surface charge density. The investigated short-range asymptotics ensures accurate calculation of the electrodipping force. For a fast and convenient application of the obtained results, the derived physical dependencies are tabulated as functions of the contact angle and the dielectric constants.

Precision of total energy and orbital energies with the expansion method for the optimized effective Kohn–Sham potential

For functionals that depend on the Kohn–Sham orbitals, the optimized effective potential method (OEP) of density functional theory (DFT) seeks a lowest energy solution by finding that particular local potential v s for which a stationary value of the energy is obtained, δ E/δ v s=0. We assess the performance of a particular method of solution, namely the expansion of v s, or the rest term v s– v 0, in a finite set of expansion functions, using the exact exchange functional (EXX) as the simplest realistic orbital dependent functional. Here, v 0 is a fixed local potential having the long-range asymptotics −1/ r. For some prototype small systems the interdependence of the basis sets for the Kohn–Sham orbitals and for the potential has been investigated, as well as the effect of the reference potential v 0. We specifically address the numerical precision with which the total energy E EXX and the orbital energies { ε i EXX } can be obtained. The EXX solution is obtained both with and without explicitly imposing the ‘HOMO condition’ that the energy ε H of the highest occupied molecular orbital be equal to the expectation value of the Fock operator. The potential expansion method yields reliable total energies even without the use of a reference potential ( v 0=0). However, the reliability of the calculated orbital energies remains a serious problem. Without the HOMO condition even the use of reference potentials with correct asymptotics cannot prevent an uncontrolled shift of the orbital energies. Imposing the HOMO condition solves this problem. But even with this condition imposed, the accuracy of other orbital energies is, typically, many orders of magnitude lower than that for the total energy.

Simple approximants for natural orbitals of harmonium

Simple approximations to the natural orbitals (NOs) of harmonium with enforced correct short- and long-range asymptotics yield accurate bounds for the NO occupancies. In particular, expressions involving Pade approximants with just one variational parameter are capable of producing the largest NO occupancies with accuracy better than 10(-4). The comparison of two cases with different coupling strengths omega (1.948 51<n<1.948 60 for omega=12 and 1.821 24<n<1.821 29 for omega=110) indicates that the bounds actually become tighter with the increasing extent of correlation. The expressions derived for the most strongly occupied NOs can be readily generalized to all natural orbitals of harmonium.

Microscopic description of a liquid–vapor interface by an inhomogeneous integral equation theory

We developed an inhomogeneous integral equation theory yielding the inhomogeneous pair correlation functions as well as the density profiles of the liquid–vapor interface of simple fluid. We analytically derived the long-range asymptotics of the inhomogeneous pair distribution along the interface, related to capillary waves. We showed that their physical nature is the same as long-range fluctuations of critical fluid which are restricted to the two-dimensional interfacial region by the external field shaping the interface.

Resonance interaction between one excited and one ground state atom

The nature of the resonance interaction between two isotropic atoms in an excited configuration is reinvestigated. The currently accepted oscillatory form for the long-range retarded resonance interaction is shown to be a subtle artefact that arises due to too drastic approximations. Formulation of the resonance interaction energy problem in terms of the interacting system leads to a form that it is ∝ r �4 in the retarded limit. We also demonstrate that the resonance interaction energy at any finite temperature goes over to purely classical long-range asymptote. This manifestation of the correspondence principle is due to thermal excitation of the electromagnetic field. We finally discuss why the textbook result for the Forster energy transfer between two atoms is incorrect for the same reasons.

Atom-atom interactions at and between metal surfaces at nonzero temperature

We have investigated the temperature-dependent Casimir-Polder interaction between two oscillators in the proximity of metal surfaces. The interaction near a single metal surface has much in common with the interaction in free space. However, at any finite temperature the long-range asymptote is equal to the high-temperature asymptote. This asymptote, which originates not from the n=0 0 term in the Matsubara summation but from thermal population of the n>0 terms, is F(R) = -2k B Tα 2 0 /R 6 . This should be compared with the more rapidly decaying zero-temperature Casimir-Polder asymptote, F(R) -13/cα 2 0 /(2πR 7 ). The interaction in the midplane between two metallic surfaces is very different. The nonretarded interaction decreases exponentially and the interaction is dominated by an enhanced Casimir-Polder-like asymptote. At large separations this asymptote also decays exponentially. For any relevant temperatures the long-range asymptote is no longer equal to the high-temperature limit. In other words crossover to a classical limit found for the long-range interaction in free space, and on a metal surface, is not always valid in a narrow cavity.

Fluctuation-multipole mechanism of intermicellar interaction in nonionic solutions

This paper continues the study of the new mechanism for long-range interparticle interactions in nonionic solutions of spherical micelles first reported in Lokotosh et al. (Colloid J. 59 (1997) 48). It takes into account that the fluctuation variations of particle's shape change the power of the surface electrical dipole layer and stimulate the appearance of non-zero electrostatic multipole moments. The contribution of the fluctuation-multipole mechanism to the interparticle potential is considered in detail. In particular, it is shown that this mechanism can lead to either attraction or repulsion depending on the ratio of dielectric constants of micelles to solvent. The comparison with long-range asymptotics of the Hamaker potential is performed. It is shown that the fluctuation-multipole mechanism dominates in many cases. Some of its characteristic applications to thermodynamic problems are considered.

Potentials of mean force of simple ions in ambient aqueous solution. I. Three-dimensional reference interaction site model approach

We adapt the three-dimensional reference interaction site model (3D-RISM) to calculate the potentials of mean force for ion–molecular solution as a difference between the chemical potential of solvation of a cluster of solutes and of individual ones. The method yields the solvation structure around the cluster of solutes in detail. The solvation chemical potential is obtained for the three-dimensional hypernetted chain (3D-HNC) closure as well as for its partial linearization (3D-PLHNC approximation). The solvation chemical potential is obtained in a closed analytical form for both the 3D-HNC and 3D-PLHNC closures. The 3D-RISM integral equations are solved by using the supercell technique. A straightforward supercell treatment of ionic solute in polar molecular solvent leads to a big error in the potential of mean force as well as the solvation chemical potential, which for simple ions in water amounts to about 35 kcal/mol. We elaborated corrections to the 3D-RISM integral equations, alleviating the artifact of the supercell periodicity with an accuracy of 0.05 kcal/mol or better and restoring the long-range asymptotics of the solute–solvent correlation functions. The dielectrically consistent site–site RISM/HNC theory (DRISM/HNC) is employed for the solvent correlations to provide a proper description of the dielectric properties of solution. This allowed us to extend the description to solution at a finite salt concentration. We converge both the 3D-RISM and site–site DRISM integral equations by using the method of modified direct inversion in the iterative subspace. Owing to the proper initial guess of the correlation functions, iteration begins at once for a given temperature and full molecular charge, avoiding a gradual decrease of the temperature and increase of the site charges, which greatly reduces the computation time. We calculate and discuss the potentials of mean force for sodium chloride in ambient water at infinite dilution as well as at a finite concentration.

Properties of electron density and other one-electron observables derived from generalized Hiller–Sucher–Feinberg identities

A generalization of the Hiller–Sucher–Feinberg (HSF) and Rassolov–Chipman identities for the electron density is presented. A companion expression for the electrostatic potential is derived. Properties of the electron density furnished by the generalized HSF identity are discussed. In particular, the behavior in the vicinity of an arbitrary potential singularity and the long-range asymptotics are analyzed in detail. A simple numerical example is provided to illustrate the new theoretical results.

Localization of a Conduction Electron Near a Semiconductor-Insulator Interface by a Charged Centre Situated in the Insulator

A conduction electron bound to a charged shallow impurity located near a semiconductor-insulator interface outside as well as inside the semiconductor is considered within the model of a hydrogen-like atom in a semi-infinite space. The problem is solved exactly including the impurity electrostatic image at the interface. The electron electrostatic image is next allowed for by the variational method. Rapidly convergent expansions of the wavefunctions are found. The discrete energy spectrum is calculated against the distance of the impurity from the interface. For the impurity located inside the semiconductor at a distance from the interface, the energy levels are lower than in the semiconductor bulk due to the impurity image, and have long-range asymptotics. Near the surface, the levels have a minimum and then rise quickly because of the spatial confining of the electron wave-function. As the impurity leaves the semiconductor and recedes from it into the insulator, the discrete levels crowd together approaching the continuum as the inverse of the distance from the surface, but they all persist for an arbitrarily remote impurity. For the impurity located in the insulator far from the semiconductor, semiclassical asymptotics of the solutions are obtained, and an approximation of the solutions in cylindrical coordinates is derived.