Prediction of the derivative discontinuity in density functional theory from an electrostatic description of the exchange and correlation potential

We propose an approach to approximate the exchange and correlation (XC) term in density functional theory. The XC potential is considered as an electrostatic potential, generated by a fictitious XC density, which is in turn a functional of the electronic density. We apply the approach to develop a correction scheme that fixes the asymptotic behavior of any approximated XC potential for finite systems. Additionally, the correction procedure gives the value of the XC derivative discontinuity; therefore, it can directly predict the fundamental gap as a ground-state property.     

Deuteron wave function and OPE potential

The deuteron wave function is calculated integrating from outside the Schredinger equation using as input its asymptotic behaviour. Some potentials are tested and the one pion exchange potential (OPEP) is shown to be the main responsible of the wave function structure up to distances of about 1 fm. The relevance of the short range part of the potential is analyzed and it is shown that a substantial enhancement of the OPEP central part is needed in the deuteron channel.     

Coulomb distortion effects on single particle exchange singularities

It is shown that Coulomb distortion modifies the single-particle exchange pole residue by a factor independent of the orbital angular momentum of the bound states involved in the exchange process. The implications of this result on the polarization observables and on recent determinations of the deuteron asymptotic D- to S-state ratio, using analyticity, are discussed.     

Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type

We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N?m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N?1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation.     

The correlation of length spectra of two hyperbolic surfaces

We derive an asymptotic formula for the number of free homotopy classes on a closed surface which have (approximately) the same length with respect to two different hyperbolic structures on the surface. The growth rate in the asymptotic formula is described in terms of the thermodynamic formalism for the geodesic flow.     

Effect of correlation and spin-polarisation on the band structure of metallic dysprosium

Energy bands of dysprosium have been calculated considering the effects of correlation and spin-polarisation. The exchange and correlation contributions to the spherically symmetric crystalline potential have been taken in the forms suggested by (i) Kohn and Sham and (ii) Overhauser. The exchange and correlation potential of von Barth and Hedin has been used to study the effect of spin-polarisation on the band structures. The resulting bandwidth, density of states, magnetic moment and spin-splitting have been computed and compared with experimental results. Some discrepancies remain; theoretical calculations done so far agree reasonably among themselves, so accurate experimental data are probably called for.     

Coulomb effects on single-particle exchange singularities

We consider the singularity in the scattering amplitude arising from the exchange of a massive neutral particle. It is shown that the presence of Coulomb distortion in the entrance or exit channel modifies the exchange pole residue. Within the framework of the Coulomb wave Born approximation the exchange pole residue is modified by an energy-dependent factor that is independent of the orbital angular momentum of the bound states involved in the exchange process. The implications of this result on the polarization observables and on recent determinations of the deuteron asymptotic D- to S-state ratio, by analytic continuation in cos θ to the neutron exchange pole, are discussed.     

Superadiabatic small-scale combustors: Asymptotic analysis of a two-step chain-branching combustion model

An asymptotic study for a counterflow burner consisting of thin channels with heat exchange is proposed. The focus is made on the cases of ultra lean burning using a model of a two-step chain-branching chemistry. The ratio of the channel length to the thermal flame thickness is used as a natural large parameter. Then, the solution is constructed by the method of asymptotic expansions using this parameter. Finally, the obtained asymptotic for the flame position is satisfactorily compared with the exact solution of the problem. These explicit results have a clear advantage in that they facilitate considerably the parametric analysis. It is demonstrated that combustion of mixtures below the flammability limit can be carried out in the considered systems.     

Calculation of the interface exchange coupling constants between Fe and FeF2-like fluorides

The interface exchange coupling between ferromagnetic (F) and antiferromagnetic (AF) materials is interesting in itself and has also attracted recent attention in relation to the exchange bias phenomenon. A major difficulty in developing a reliable exchange bias theory lies in the fact that both the F and AF interface characteristics (geometry and physical parameters) are hard to determine experimentally and complicated to estimate theoretically. We adopt in this paper two alternative interface configurations to obtain upper and lower bounds for the computed values of the exchange coupling across the interface between metallic Fe and insulating FeF₂, derived on the basis of ab initio calculations implemented for a periodic supercell. Electronic structures and total energies were computed within density functional theory using the generalized gradient approximation for the exchange correlation potential. We expect the results obtained to be useful in model simulations with larger unit cells and non-collinear spins.     

Semiclassical neutral atom as a reference system in density functional theory

We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.     

Asymptotic expansion of the heat kernel trace of Laplacians with polynomial potentials

It is well known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemannian manifolds can be obtained through termwise integration of the asymptotic expansion of the on-diagonal heat kernel. The purpose of this work is to show that, in certain circumstances, termwise integration can be used to obtain the asymptotic expansion of the heat kernel trace for Laplace operators endowed with a suitable polynomial potential on unbounded domains. This is achieved by utilizing a resummed form of the asymptotic expansion of the on-diagonal heat kernel.     

Extreme-value dependence: An application to exchange rate markets

Extreme value theory (EVT) focuses on modeling the tail behavior of a loss distribution using only extreme values rather than the whole data set. For a sample of 10 countries with dirty/free float regimes, we investigate whether paired currencies exhibit a pattern of asymptotic dependence. That is, whether an extremely large appreciation or depreciation in the nominal exchange rate of one country might transmit to another. In general, after controlling for volatility clustering and inertia in returns, we do not find evidence of extreme-value dependence between paired exchange rates. However, for asymptotic-independent paired returns, we find that tail dependency of exchange rates is stronger under large appreciations than under large depreciations.     

铁磁-p波超导结中的自旋极化隧道谱与散粒噪声

考虑到界面的势垒散射和铁磁层中的磁交换作用，依照Sr2RuO4超导体具有自旋三重配对态的p波对称结构，研究铁磁-p波超导结中的自旋极化隧道谱与散粒噪声，研究表明：1.对于幺正配对态，随着铁磁层中磁交换劈裂增强，隧道谱与散粒噪声都减少；2.对于非幺正配对态，隧道谱与散粒噪声都依赖于铁磁层的磁化轴方向，当磁化轴平行于非幺正配对态的自旋轴时，在低偏压下磁交换作用能使隧谱与散粒噪声增强，而当磁化轴反平行于自旋转轴时，其结果相反。     

Josephson effect in superconducting hybrid S/F structures with parallel and antiparallel magnetizations of the ferromagnetic layers

The Josephson effect in S-MB-S, S/F-MB-S, and S/F-MB-F′/S superconducting hybrid structures with the parallel or antiparallel orientation of exchange fields in the layers of metal ferromagnets (F and F′) and in the magnetic barrier (MB) with arbitrary transparency has been investigated. It has been shown that the properties of the studied structures depend strongly on the orientation of the exchange fields: the exchange-field-induced stimulation of the critical current is possible for one orientation, whereas the critical current is suppressed at the opposite orientation of the exchange fields. A change in the orientation of the exchange fields can lead to the switching of the Josephson structures between 0 and π states. The effect of the pair-breaking mechanisms on the Josephson effect and on the spectrum of the Andreev levels in the S-MB-S structures has been analyzed. The results indicate the possibility of stimulating the critical current by the external magnetic field in the S-MB-S structures with thin-film superconducting banks.     

有缓冲层的多层金属包层介质光波导的渐近展开方法

提出求解有缓冲层的多层金属包层介质光波导的一个准解析方法，它应用渐近开展理论将传播常数展开成一个小参数的级数，这一方法本身是精确的，它能达到任意所需的精度，然而四层和五层波导结构的数值计算实例表明，仅二阶近似解就足够精确了。这一方法的优点是简单并且不同层数波导结构以及ＴＥ和ＴＭ膜的解有相同的表达式形式。     

Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + ¹²C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.     

Exchange mechanism of dα interaction and vertex constants of <Superscript>6</Superscript>Li

In this work, we use a model for describing the dα interaction in a ⁶Li nucleus, in which the dα nuclear potential is written as the sum of the local folding potential and a nonlocal term originating from the deuteron exchange mechanism and corresponding to a three-deuteron component of the ⁶Li wave function. This model was used to calculate the nuclear vertex constants and the corresponding asymptotic normalization coefficients of ⁶Li in the dα channel. Both values L = 0 and L = 2 of relative dα orbital angular momentum L were considered. Calculations were performed with and without allowance for the Coulomb dα interaction.