First principles calculations of the volume dependence of the spin susceptibility for Li and Na

The new variational principle-density functional theory of the spin susceptibility has been used to calculate its volume dependence for Li and Na. The results are compared with recent experiments and previous theories. The exchange-correlation functionals are treated in the local spin density approximation. The single particle electron states are treated in the spherical cell approximation. The agreement between the new theory and experiment is very good for Na and quite acceptable for Li when OPW values of the single particle density of states are used. The results of the new theory are superior to those of the previous theories.     

The second-order Rytov approximation and residual error in dual-frequency satellite navigation systems

The second-order Rytov approximation has been used to determine ionospheric corrections for the phase path up to third order. We show the transition of the derived expressions to previous results obtained within the ray approximation using the second-order approximation of perturbation theory by solving the eikonal equation. The resulting equation for the phase path is used to determine the residual ionospheric first-, second- and third-order errors of a dual-frequency navigation system, with diffraction effects taken into account. Formulas are derived for the biases and variances of these errors, and these formulas are analyzed and modeled for a turbulent ionosphere. The modeling results show that the third-order error that is determined by random irregularities can be dominant in the residual errors. In particular, the role of random irregularities is enhanced for small elevation angles. Furthermore, in the case of small angles the role of diffraction effects increases. It is pointed out that a need to pass on to diffraction formulas arises when the Fresnel radius exceeds the inner scale of turbulence.     

An integral equation theory for the dense dipolar hard-sphere fluid

An integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres. The pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results. The dielectric constant in this approximation is larger than that predicted by previous theories.     

An application of second order approximations for the Green's function

In a previous paper there was developed an approximation theory for the Green's functions which gives approximations consistent with the conservation laws of the Hamiltonian. We have chosen a concept of reduction which is different and which leads to other approximations for the particle-hole Green's function than the usual concept of reduction. The particle-hole Green's function is the function $$\langle \Psi _0 |\tau \{ a_1^ + (0)a_2 (0)a_3^ + (t)a_4 (t)\} |\Psi _0 \rangle $$ where ¦Ψ_o〉 is the real ground state and τ stands for the time ordered products of the operators. Now, in this paper we want to give an example of an application of this theory. We present a second order approximation since the first order approximation is the well known Random Phase Approximation.     

Triviality of Quantum Electrodynamics Revisited

Quantum electrodynamics is often considered to be a trivial theory.This is based on a number of evidences,both numerical and analytical.One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling.We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections,the Landau pole is removed.We also analyze the cutoff dependence of the bare coupling at two-loop order and conclude that the conjecture,that for reasons of self-consistency,QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.     

Structure and thermodynamics of polar interaction site fluids

We present results for the structure and thermodynamics of the dipolar hard dumbbell fluid obtained from a recently developed theory which is based on an extension of cluster perturbation theory (CPT) for atomic fluids to the interaction site formalism. The calculations are for the lowest order result in the theory which we denote as the optimized random phase approximation in the interaction site formalism (ISF-ORPA). This method does not include unallowed diagrammatic contributions to the structure and thermodynamics, in contrast to previous CPTs in the interaction site formalism. We compare the results to computer simulation data and find that the theory gives a realistic representation of the effect of the electrostatic interactions on the structure of the fluid.     

Theory of Stark broadening—I soluble scalar model as a test

The purpose of the present paper is to test, on an exactly soluble model, the validity of standard approximations used in the theory of Stark broadening of atomic lines. The mathematical treatment involves no approximation; in particular, overlapping and incomplete collisions are correctly taken into account. In setting up the model, standard physical approximations are made: the dipole approximation, and uncorrelated perturbers with classical paths. In addition, in order to permit exact solution, the problem is taken to be scalar.     

液体理论中的Kirkwood变分方法的推广

本文克服了Cohen理论的缺点,对液体理论中Kirkwood变分方法作了推广。经过这样推广,格胞模型理论就可以系统地考虑分子运动关联性的任何级近似。把所得结果应用到一维情形,得到的自由能是严格正确的。应用到三维情形,最低级近似得LJD结果,一级近似得Taylor结果。     

On the energy loss of high energy quarks in a finite-size quark-gluon plasma

The induced gluon emission from a fast quark passing through a finite-size QCD plasma is studied within the light-cone path integral approach. It is shown that the leading log approximation used in previous studies fails when the gluon formation length becomes on the order of the length of the medium traversed by the quark. Calculation of the energy loss beyond the leading log approximation gives the energy loss which grows logarithmically with quark energy, contrary to the energy-independent prediction of the leading log approximation.     

Modelling of a displacive transformation in two-dimensional system within four-body approximation of Continuous Displacement Cluster Variation Method

Following our previous study on distorted to non-distorted displacive phase transformation in the two-dimensional square lattice based on the continuous displacement cluster variation method (CDCVM) within the Bragg–Williams (BW) approximation, we performed a higher order approximation, four-body approximation, in the entropy term and compared the results obtained by the two approximations. The transformation temperature decreases with the higher order approximation, which shares the common feature with conventional CVM studies on replacive transformations. The present study predicts the first-order transformation, which is markedly different from the previous study based on the BW approximation. Furthermore, by employing the four-body approximation, we are able to reproduce the o-type distribution of displaced atoms around a Bravais lattice point by changing the atomic interaction energy, which was by no means possible by the BW approximation.     

Self-consistent treatment of a phase transition in a system with a vector order parameter

The problem of the continuation of the Hartree approximation below the transition temperature is considered for a system with a vector order parameter, In contrast to the case of a scalar order parameter, considered in a previous paper, it is found that a self-consistent and gapless approximation can be constructed in the limit of a very large number of vector components. The results agree with those of the spherical model.     

Graphical representation of perturbation theory for line spectra

A graphical method is given for representing any approximation in Shrödinger's perturbation theory for the energy and wave function of a nondegenerate state; the previous approximations do not have to be formulated in detail.     

Some aspects of the theory of defects of ordered media and gauge fields related to foliations

When translational symmetry is broken in the ground state, the homotopy theory of defects of ordered media has to be supplemented with integrability conditions, coming from the theory of foliations. These show how some homotopy classes split into several distinct defects, while other homotopy classes do not occur physically. This framework can also be used in order to discuss defects of gauge fields, where in a first approximation classifying spaces play the role of the manifolds of internal states.     

First Order Approximation of the 5-dimensional Projective Unified Field Theory

The new version of a 5-dimensional Projective Unified Field Theory is presented up to the first order approximation with respect to the gravitational constant and referring to nonrelativistic velocities. Since exact solutions of this theory can only be found for exceptional cases, this approximation procedure provides a practicable approach to physical applications of the theory.     

Finite-temperature Hartree-Fock approximation to λΦ4 theory

The finite-temperature Hartee-Fock approximation to the effective potential for massless λΦ⁴ theory is calculated. The reflection symmetry which, in the same approximation, turns out to be spontaneously broken at zero temperature, is restored at a critical temperature. The nature of the phase transition is analyzed. A comparison with previous calculations is presented.     

Thermal fluctuations of a quantized electromagnetic field in weakly absorbing media

The quantum fluctuations of an electromagnetic field in thermally excited media are calculated using the quantum electrodynamical method of Γ operators and without invoking phenomenological elements. The drawbacks of the standard theory based on the fluctuation-dissipation theorem and on the Matsubara technique of temperature Green’s functions are indicated. The decisive role of the correct consideration of higher order photon-photon correlators and the inadmissibility of their approximation by products of lower order correlators are underlined. It is shown that, contrary to the accepted opinion, the quantum fluctuations of an electromagnetic field cannot be expressed via the refractive indices of media introduced into the theory for the calculation of mean fields. The results obtained are compared with those previously derived using the Matsubara technique for calculation of the Green’s functions of an electromagnetic field in dispersive media under conditions of thermodynamic equilibrium. The previous results are shown to be incorrect at least for media consisting of atoms or molecules with a discrete energy spectrum.     

On the post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble theory

The post-Newtonian approximation of the Einstein-Cartan-Sciama-Kibble or ECSK theory is developed. It is used to obtain a drastic reduction on the density of the source needed to detect the spin. It is also proved that if we know the structure of the source, up to order ¯v, the spin can be detected, and if we know it up to order ¯v² the theory can be verified.Supported by a scholarship from the Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET).     

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb Systems. III. Loopwise Expansion

We present an exact field theoretical representation of an ionic solution made of charged hard spheres. The action of the field theory is obtained by performing a Hubbard–Stratonovich transform of the configurational Boltzmann factor. It is shown that the Stillinger–Lovett sum rules are satisfied if and only if all the field correlation functions are short range functions. The mean field, Gaussian and two-loops approximations of the theory are derived and discussed. The mean field approximation for the free energy constitutes an exact lower bound for the exact free energy, while the mean field pressure is an exact upper bound. The one-loop order approximation is shown to be identical with the random phase approximation of the theory of liquids. Finally, at the two-loop order and in the pecular case of the restricted primitive model, one recovers results obtained in the framework of the mode expansion theory.