Coulomb Systems with Ideal Dielectric Boundaries: Free Fermion Point and Universality

A two-component Coulomb gas confined by walls made of ideal dielectric material is considered. In two dimensions at the special inverse temperature =2, by using the Pfaffian method, the system is mapped onto a four-component Fermi field theory with specific boundary conditions. The exact solution is presented for a semi-infinite geometry of the dielectric wall (the density profiles, the correlation functions) and for the strip geometry (the surface tension, a finite-size correction of the grand potential). The universal finite-size correction of the grand potential is shown to be a consequence of the good screening properties, and its generalization is derived for the conducting Coulomb gas confined in a slab of arbitrary dimension 2 at any temperature.     

Field theoretical approach to inhomogeneous ionic systems: thermodynamic consistency with the contact theorem,Gibbs adsorption and surface tension

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Hückel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.     

电子关联效应对平行双量子点系统磁输运性质的影响

从理论上研究了平行双量子点系统中的电子关联效应对该系统磁输运性质的影响. 基于广义主方程方法, 计算了通过此系统的电流、微分电导和隧穿磁阻. 计算结果表明: 电子自旋关联效应可以促发一个很大的隧穿磁阻, 而电子库仑关联效应不仅可以压制电子自旋关联效应, 还可以导致负隧穿磁阻和负微分电导的出现. 对相关的基本物理问题进行了讨论.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. I. Mean-Field Scheme

The equilibrium density profiles in a classical multicomponent plasma near a hard wall made with a dielectric material characterized by a relative dielectric constant ∈_w are studied from the first Born–Green–Yvon (BGY) equation combined with Poisson equation in a regime where Coulomb coupling is weak inside the fluid. In order to prevent the collapse between charges with opposite signs or between each charge and its dielectric image inside the wall when ∈_w>1, hard-core repulsions are added to the Coulomb pair interaction. The charge-image interaction cannot be treated perturbatively and the density profiles vary very fast in the vicinity of the wall when ∈_w≠1. The formal solution of the associated inhomogeneous Debye–Hückel equations will be given in Paper II, together with a systematic fugacity expansion which allows to retrieve the results obtained from the truncated BGY hierarchy. In the present paper the exact density profiles are calculated analytically up to first order in the coupling parameter. The expressions show the interplay between three effects: the geometric repulsion from the impenetrable wall; the electrostatic effective attraction (∈_w>1) or repulsion (∈_w<1) due to its dielectric response; and the Coulomb interaction between each charge and the potential drop created by the electric layer which appears as soon as the system is not symmetric. We exhibit how the charge density profile evolves between a structure with two oppositely-charged layers and a three-layer organization when ∈_w varies. (The case of two ideally conducting walls will be displayed elsewhere).     

Two-Dimensional Coulomb Systems on a Surface of Constant Negative Curvature

We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to zero at infinity. The pressure can be expanded as a series in integer powers of the density (the virial expansion). The correlation functions have a thermodynamic limit, and remarkably that limit is the same one for the Coulomb interaction and some other interaction law. However, special care is needed for defining a thermodynamic limit of the free energy density. There are sum rules expressing the property of perfect screening. These generic properties can be checked on the Debye–Hückel approximation, and on two exactly solvable models, the one-component plasma and the two-component plasma, at some special temperature.     

Coulomb energy of nuclei

The density functional determining the Coulomb energy of nuclei is calculated to the first order in e ². It is shown that the Coulomb energy includes three terms: the Hartree energy; the Fock energy; and the correlation Coulomb energy (CCE), which contributes considerably to the surface energy, the mass difference between mirror nuclei, and the single-particle spectrum. A CCE-based mechanism of a systematic shift of the single-particle spectrum is proposed. A dominant contribution to the CCE is shown to come from the surface region of nuclei. The CCE effect on the calculated proton drip line is examined, and the maximum charge Z of nuclei near this line is found to decrease by 2 or 3 units. The effect of Coulomb interaction on the effective proton mass is analyzed.     

Density Profiles in a Classical Coulomb Fluid Near a Dielectric Wall. II. Weak-Coupling Systematic Expansions

In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer diagrams for the fugacity expansions of the densities, we exhibit how the long-range of both the self-energy and pair interaction are exponentially screened at large distances from the wall. However, the self-energy due to Coulomb interaction with images still diverges in the vicinity of the dielectric wall and the variation of the density is drastically different at short or large distances from the wall. This variation is involved in the inhomogeneous Debye–Hückel equation obeyed by the screened pair potential. Then the main difficulty lies in the determination of the latter potential at every distance. We solve this problem by devising a systematic expansion with respect to the ratio of the fundamental length scales involved in the two coulombic effects at stake. (The application of this method to a plasma confined between two ideally conducting plates and to a quantum plasma will be presented elsewhere). As a result we derive the exact analytical perturbative expressions for the density profiles up to first order in the coupling between charges. The mean-field approach displayed in Paper I is then justified.     

General Decomposition of Radial Functions on Rn and Applications to N-Body Quantum Systems

We present a generalization of the Fefferman–de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions V on Rⁿ going to zero at infinity. This generalized decomposition can be used to extend previous results on N-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application, we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.     

Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063.     

Two-dimensional models for an electrode with adsorption sites

Through a new method, the following model is solved exactly in the framework of classical equilibrium statistical mechanics of two-dimensional Coulomb systems, for the special value=2 of the coupling constant: the mobile charges of a one-component plasma are attracted by a line of equidistant sticky adsorption sites embedded in a background, the density of which varies in the direction orthogonal to the line. First the general expressions are given for the densities and correlation functions of nonadsorbed and adsorbed particles. Then these results are used to investigate two models of electrodes with localized adsorption: the externally charged hard wall and the impermeable polarized membrane. In each case the influence of the adsorption upon macroscopic features is studied: the potential drop across the interface, the contact theorem, and the Lippmann equation, which involves the surface free energy.     

Classical Coulomb systems near a plane wall. II

The equilibrium structure of classical Coulomb systems bounded by a plane hard wall is studied near that wall. A general sum rule is derived for the asymptotic form of the charge-charge correlation function along the wall. The exact results which can be obtained for the two-dimensional one-component plasma provide a test for this new sum rule, as well as for other already known sum rules or their generalizations.This laboratory is associated with the Centre National de la Recherche Scientifique.     

Spatial correlations in the electron gas: Path integral Monte Carlo simulation

Thermally excited states of the three-dimensional electron gas in a neutralizing background are computed by path integral Monte Carlo simulation for values of the Wigner-Seitz radius within the interval 5 < r _s < 15. Coulomb and exchange interactions, permutation symmetry, and spin state are treated explicitly. Variation of electron correlation functions with density and temperature is analyzed. Quantum effects suppress and enhance spatial correlation at low and high densities, respectively. Transition between the electron-gas states characterized by these opposite trends corresponds to a density of approximately 2.5 × 10²¹ cm^?3. A transition line between liquid-like and gaslike phases is determined in the temperature-density diagram. Weak anisotropy of many-body correlations in the liquid-like state stimulates excitation of spherically symmetric collective rotational modes. The effective short-range pseudopotential exhibits strong temperature dependence due to exchange effects. For strongly correlated systems, the characteristic screening length deviates from that predicted by the Thomas-Fermi screening model ( $ \sim \sqrt {r_s } $ ), approaching a linear function of r _s. The effective short-range interaction substantially differs from the Yukawa potential in mean field theory. Coulomb interaction shifts the Fermi level up by an order of magnitude or higher, and this effect becomes stronger with decreasing density.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation

This paper concerns the equilibrium bulk charge and current density correlation functions in quantum media, conductors and dielectrics, fully coupled to the radiation (the retarded regime). A sequence of static and time-dependent sum rules, which fix the values of certain moments of the charge and current density correlation functions, is obtained by using Rytov’s fluctuational electrodynamics. A technique is developed to extract the classical and purely quantum-mechanical parts of these sum rules. The sum rules are critically tested in the classical limit and on the jellium model. A comparison is made with microscopic approaches to systems of particles interacting through Coulomb forces only (the non-retarded regime). In contrast with microscopic results, the current-current density correlation function is found to be integrable in space, in both classical and quantum regimes.     

Towards a microscopic theory of wetting by ionic solutions. I. Surface properties of the semi-primitive model

As a first step towards a density functional theory (DFT) of wetting by ionic solutions we examine the density profiles of ions and solvent molecules confined near a charged wall, or between two walls, and the corresponding interfacial properties, including adsorption, surface tension, solvation force and electrostatic properties, within the semi-primitive model (SPM) of solutions made up of hard sphere solvent particles and charged hard spheres. Both monovalent and divalent cations with species-dependent diameters are considered. The density functional includes the best available Rosenfeld hard-sphere functional, as well as mean-field and Coulomb correlation contributions. The simpler mean-field functional is found to be adequate, at least for monovalent ions. The size differences lead to an interesting ‘fine structure’ of the density and charge density profiles. Cohesive interactions between all species are shown to lead to significant changes in the density profiles.     

基于折叠势的两势方法系统研究质子放射性(英文)

基于两势方法系统地研究了质子数51 ≤ Z ≤ 83质子放射性核素的衰变半衰期。总的质子-子核相互作用势包括:通过单折叠子核密度和DDM3Y有效相互作用得到的微观核势,通过单折叠子核电荷密度和质子-质子库仑相互作用得到的真实库仑势以及离心势。同时,预测了同一区域16个核的质子放射性半衰期,并且预测的质子放射性半衰期在4.11倍的范围内。此外,还研究了质子放射性的Geiger-Nuttall定律。结果表明,Geiger-Nuttall定律可以用来描述角动量相同的同位素的质子放射性。In the present work, we systematically study the half-lives of proton radioactivity for 51 ≤ Z ≤ 83 nuclei within the two-potential approach. The total emitted proton-daughter nucleus interaction potential is composed of the microscopic nuclear potential obtained by single folding the density of the daughter nucleus with the DDM3Y effective interaction, the realistic Coulomb potential obtained by single folding the charge density of the daughter nucleus with the proton-proton Coulomb interaction and the centrifugal potential. We extend our study to predict proton radioactivity half-lives of 16 nuclei in the same region within a factor of 4.11. In addition, the Geiger-Nuttall law for proton radioactivity is researched. The results indicate that the Geiger-Nuttall law can be used to describe the proton radioactivity isotopes with same angular momentum.     

修正屏蔽库仑势下二维尘埃等离子体的动力学和结构特性

本文考虑等离子体密度分布变化, 得到了修正屏蔽库仑势的解析解. 数值分析以及分子动力学模拟表明, 在常见实验室参数情况下, 等离子体密度分布变化引起的屏蔽库仑势修正对二维尘埃等离 子体系统的动力学和结构特性影响很小. 在极限参数情况下, 本模型的计算结果表明二维尘埃等离子体系统的扩散能力明显降低, 并且系统组态呈圆形分布. 此外, 本文还研究了实验室常见大小磁场对二维尘埃等离子体系统的影响. 关键词： 修正屏蔽库仑势 二维尘埃等离子体 分子动力学模拟     

Charge Correlations in a Coulomb System Along a Plane Wall: A Relation Between Asymptotic Behavior and Dipole Moment

Classical Coulomb systems at equilibrium, bounded by a plane dielectric wall, are studied. A general two-point charge correlation function is considered. Valid for any fixed position of one of the points, a new relation is found between the algebraic tail of the correlation function along the wall and the dipole moment of that function. The relation is tested first in the weak-coupling (Debye–Hückel) limit, and afterwards, for the special case of a plain hard wall, on the exactly solvable two-dimensional two-component plasma at coupling =2, and on the two-dimensional one-component plasma at an arbitrary even integer .     

Coulomb screening effects on the optoelectronic far-infrared properties of spatially separated few-layer graphene

We investigate the longitudinal optical conductivity of spatially separated few-layer graphene analytically and numerically. Each layer could be monolayer or bilayer graphene. The density–density correlation function has been screened by the dielectric function using the random phase approximation, which includes the inter-layer Coulomb coupling. In the presence of the potential function between the layers, the carrier densities in each layer can be tuned respectively. In these two-dimensional layered structures, the main contributions to the optical conductivity are from the intra- and inter-band transition channels in a same layer. In the infrared region, the Drude optical conductivity was observed by the unscreened intra-band transition process. But in the presence of the inter-layer Coulomb interaction, one peak structure of the optical conductivity is observed which can be modified by the dielectric environment. From the number of turning points and the turning positions, the carrier density, the Fermi wavevector, and the layered structure can be determined.     

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath     

The effect of 4d states based full Heusler alloy on the electronic and magnetic properties of new half metallic ferromagnetism: DFT+U study

A full heusler alloy Ru₂MoSb is studied using the full potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT). Structural, electronic and magnetic properties are investigated for this material. We have used the generalized gradient approximation of Perdew, Burke, and Ernzerh (GGA-PBE), the GGA+U and the modified Becke–Johnson potential of GGA+U (mBJ-GGA+U) to model exchange correlation potential. The Hubbard on-site Coulomb interaction correction U is calculated by constraint local density approximation for both 4d elements Ru and Mo.For both approximations GGA+U and mBJ- GGA+U, density of states and band structure reveal that our compound has a half-metallic character. Magnetic properties show that Ru₂MoSb is ferromagnetic with an integer magnetic moment of 3 µB which is in good agreement with the Slater–Pauling rule. The half-metallicity of Ru₂MoSb is stable under lattice constant changes which makes it a potential contender for spintronic applications.The negative values of the cohesion energy and the formation energy indicate that our Heusler alloy can be synthesized and stabilized experimentally.