Self-consistent Integral Equation Research Articles

Local-field study of the optical second-harmonic generation in a symmetric quantum-well structure.

A nonlocal analysis of the infrared second-harmonic generation associated with intersubband transitions in a symmetric semiconductor quantum-well structure is presented. Taking as a starting point a fundamental self-consistent integral equation for the local field, the p-polarized first-harmonic field inside the quantum well is studied. By using the infinite-barrier wave functions and taking into account only the two lowest subbands, analytical expressions are obtained for the local field. The result of the local-field calculation at the first-harmonic frequency, in turn, is used to calculate the p-polarized second-harmonic local field. The conversion efficiency of the second-harmonic generation from the quantum well is thus determined. Numerical calculations of the frequency and angular spectra of the second-harmonic intensities are presented for a symmetric GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum well. The numerical results show that strong second-harmonic generation occurs in the vicinity of the resonance frequencies for both the first- and second-harmonic local field inside the quantum well. The influence of the dynamic local-field interaction of the electrons on the optical second-harmonic generation is investigated. It is demonstrated that the dynamic screening can lead to a notable upward shift of the locations of the resonant peaks in the frequency spectra of the second-harmonic conversion coefficient.

A self-consistent determination of the atomic and electronic structure of a model liquid metal

Based on a Lennard-Jones two-body interatomic potential supplemented by a tight-binding description of the valence electron band structure, we propose an iterative scheme for the self-consistent determination of the atomic and electronic structure of a model liquid metal. The procedure makes use of recent liquid-state theories of the electronic density of states, modern thermodynamically self-consistent integral equation theories of atomic structure, and ideas from tight-binding bond theory. Results are presented and discussed for several phase points of the model system.

How reliable is the HMSA integral equation for the pair structure of supercooled and amorphous mixtures?

Accurate molecular dynamics (MD) calculations on highly asymmetric Lennard-Jones mixtures have been performed to check in rather extreme cases the ability of the self-consistent HMSA integral equation to predict the pair correlations in supercooled and glassy mixtures. We find that, in the supercooled region, the HMSA is a reasonable approximation for the structural properties and thermodynamic properties, but systematic deviations from MD data appear when the glass transition is approached.

Self-consistent integral equation theory for the equilibrium properties of polymer solutions

Self-consistent RISM integral equation theory of polymeric liquids is used to investigate the equilibrium properties of polymer solutions and melts. Density functional formalism is employed to derive the effective medium-induced potential between two sites on a polymer chain. The resulting expression leads to a coupling between the interchain and intrachain pair correlation functions. An approximate method for the calculation of the effective intrachain pair correlations is examined. The method employs Monte Carlo computer simulations of a single polymer chain interacting via local chemical interactions, long-range excluded volume, and the self-consistently determined medium-induced potential in the condensed phase to compute the intrachain pair correlations which are consistent with the interchain packing. Results for solutions of tangent hard-sphere chains are compared to recent off-lattice Monte Carlo simulations for various chain lengths and densities. In particular, it was found that the theory slightly overestimates the average size of the polymers in solution, while the density dependence of the average size of the chains is in good agreement with the Monte Carlo simulations. The inclusion of the self-consistent determination of the intrachain correlations is found to significantly alter the interchain pair correlation function at low and intermediate densities.

Photon drag in a single-level metallic quantum well.

A theoretical study of the photon-drag effect in a one-level metallic quantum well is presented. It is demonstrated that the photon drag, associated with second-order nonlinearities in the two-dimensional electron-gas system, originates in a combined diamagnetic and paramagnetic response. The photon-drag current density along the quantum well and the prevailing dc electric field across the well are calculated in a manner which takes into account local-field effects in the induced dc field as well as in the fundamental field of light. The local-field phenomena at the excitation frequency are studied on the basis of a self-consistent integral equation formalism

An effective EXP-6 potential energy function for pure nitrogen

An effective EXP-6 potential for pure nitrogen has been obtained from a comparison of calculated results, using the variational perturbation theory of Ross, with the experimental data of sound velocity and of density. The self-consistent integral equation theory of Zerah and Hansen has also been applied, using this potential, to calculate the density of nitrogen at various temperatures and up to very high pressures. The discrepancy between the two theories was found to be about 1% in an extensive range of temperature and pressure. Within the same theoretical context this potential yields better results than the previously proposed EXP-6 potentials.

Computation of the energy V of an excess electron in dense helium and argon

In this article we present a method and results for the computation of the energy of the ground state of an excess electron in undisturbed helium and argon configurations at various densities. To reproduce experimental data of the excess electron–argon system, the interactions between the induced dipoles of the argon atoms have been taken into account. These interactions were included through an effective screening function. The effective screening function used was a simple approximation to the exact result obtained by computing the electric fields at the particles self-consistently. The latter screening function is similar to a screening function calculated from the radial distribution function via a self-consistent integral equation as will be shown.

Re-Analysis of the Laser Model in Thermofield Dynamics

A generalization of the Thermofield Dynamics formalism to non-equilibrium situations is usefully applied to the study of the classic laser model which is an open system of atomic electrons and coherent photons in contact with a thermal reservoir. Novel time-dependent solutions for the coherent photon mode are found in the form of a self-consistent integral equation. The classic laser solution is shown to emerge for a special choice of the initial conditions. Other solutions are also classified by the initial conditions of the model. Physical discussions are presented.

Re-Analysis of the Laser Model in Thermofield Dynamics

A generalization of the Thermofield Dynamics formalism to non-equilibrium situations is usefully applied to the study of the classic laser model which is an open system of atomic electrons and coherent photons in contact with a thermal reservoir. Novel time-dependent solutions for the coherent photon mode are found in the form of a self-consistent integral equation. The classic laser solution is shown to emerge for a special choice of the initial conditions. Other solutions are also classified by the initial conditions of the model. Physical discussions are presented

Self-consistent polymer integral equation theory: Comparisons with Monte Carlo simulations and alternative closure approximations

Recently, Schweizer, Honnell, and Curro reported a self-consistent formulation of the polymer reference interaction site model (PRISM) theory for polymer melts. The purpose of this paper is to compare the predictions of this theory to Monte Carlo simulations of hard chains thereby allowing an independent test of the various approximations in the PRISM theory. We find that the self-consistent PRISM theory with the Percus–Yevick (PY) closure is very accurate for both the intramolecular and intermolecular correlations in hard 20-mers for a wide range of densities. The accuracy of the theory for longer chains is somewhat diminished. We also compare the PRISM theory predictions using the PY, hypernetted chain (HNC), and Martynov–Sarkisov (MS) atomiclike closures. All the closures give equally good predictions at high densities, but the HNC and MS closures exhibit unphysical features, and ultimately fail to converge, at lower densities and/or large chain lengths.

Response functions for multicomponent plasmas. II. Velocity-average approximation and dynamical mean-field theory for strong coupling.

We establish the multispecies generalization of the velocity-average formalism for the calculation of plasma response functions at arbitrary values of the coupling. We use a set of pseudopotentials rather than the bare Coulomb potential to represent the interaction between the particles in order to describe quantum effects due to the formation of bound states, diffraction, inner-shell-electron exchange, etc. The result is a self-consistent integral equation for the partial response functions

Spinodal instability of suspensions of large spheres in a fluid of small spheres

Numerical solutions of the thermodynamically self-consistent RY integral equation for the pair structure of a binary fluid hard sphere mixture, of size ratio sigma 1/ sigma 2=0.1, exhibit divergent concentration fluctuations when the partial packing fractions of the two species comparable, i.e. at low concentration of large spheres. This spinodal instability is studied at constant pressure, and it is shown that phase separation sets in for a reduced pressure P*=P alpha 13/kBT in the range 10-2<P*<10-1.

Mean-field correlations in the core of rich galaxy clusters

We develop a theory for the contribution to the clustering correlation function from gravitational interactions of neighboring pairs of galaxies in clusters. This is based on the «Hypernetted Chain Equation», a self-consistent integral equation relating the correlation function to the interaction potential.

Dynamical mean-field theory for Coulomb systems: A novel approach.

We develop a novel approach to dynamical particle correlations in a classical one-component plasma system. A self-consistent integral equation is obtained for the dynamical local field to be determined. We show that this dynamical local field possesses the following properties: (i) it simultaneously satisfies the conservation and compressibility sum rules; (ii) it has the requisite constant values depending on frequency for large wave numbers; and (iii) it develops an algebraic tail in the high-frequency limit for small wave numbers.

The pair distribution functions of the liquid alkali metals: Comparison between the VMHNC theory and molecular dynamics simulations

We discuss the application of a recently proposed thermodynamically self-consistent integral equation, the variational modified hypernetted chain (VMHNC) approximation, to the study of the structural properties of liquid metals. We show a comparison between the structure of the liquid alkali metals, as obtained within the VMHNC, and molecular dynamics simulations carried out using the same potentials and parametrization. The results show that the VMHNC is an accurate approximation for the study of the structure of liquid metals.

Self-consistent integral equation applied to the highly charged primitive model

We apply the mixed integral equation (ZH) proposed recently by Zerah and Hansen to highly asymmetrical polyelectrolytes within the primitive model. The closure interpolates continuously between the Percus–Yevick and the hypernetted chain closures for charges of same sign and between the HNC and mean spherical approximations for charges of opposite sign. The thermodynamic consistency between the virial and compressibility equations of state is obtained by varying the single parameter in the switching functions. In weakly screened and highly charged suspensions, the new ZH equation improves appreciably the HNC results. The structure factors are essentially modified in the infinite wavelength limit. The two-phase region in the phase diagram is shifted towards the low temperature or the high charge region which allows us to study more asymmetrical systems than with the HNC equation. Since no simulation data are available, the ZH equation is useful to quantify the accuracy of the HNC closure for such systems.

Soft-sphere model for the glass transition in binary alloys: Pair structure and self-diffusion.

Molecular-dynamics simulations have been carried out on a ``soft-sphere'' model for binary alloys quenched into supercooled and amorphous states. The main emphasis of the work is on the static and dynamic characterization of the glass transition. A comparison between molecular-dynamics data and the results of a self-consistent integral equation shows that the equation of state bifurcates into ``glass'' and ``fluid'' branches below a glass transition temperature ${T}_{g}$. The static pair structures differ significantly along the two branches. The structurally relaxed ``fluid'' branch leads to a phase separation at very low temperatures. Close to the glass transition, the atomic mean-square displacements of the two species go over more and more slowly to the asymptotic diffusive regime, due to the emergence of an intermediate time scale linked to the slowing down of structural relaxation. The diffusion constants of the two species follow closely a scaling law, as predicted by mode-coupling theory, except in the immediate vicinity of the glass transition where activated processes lead to residual diffusion.

A statistical theory of elastic materials with micro-defects

A statistical continuum elastic multipole modelling for the treatment of the mechanical properties of elastic materials with statistically distributed micro-defects is developed. It is shown that each kind of statistical distribution of discrete micro-defects may be represented approximately by a corresponding distribution of statistical continuum elastic multipoles and that all micro-defects can be treated in a uniform way. Two applications are given. The first treats the interaction problem of a macrocrack with a field of microcracks in an elastic solid. A generalized self-consistent linear integral equation for the determination of the effective (ensemble average) stress field is derived. The second is concerned with the determination of effective elastic moduli of materials with statistically distributed inhomogeneous volume defects.

Toward a liquid-state theory with accurate critical-region behavior

A scaling-theory approach that yields the scaled thermodynamics in the critical region as the solution of an ordinary differential equation is given, along with a power-series “isocline” representation of the solution yielding a polynomial fit of a high accuracy. A means of extending the approach to the whole liquid-state region through a self-consistent integral equation for the radial distribution function is discussed. An alternative integral-equation approach and a simple application of scaling-theory results that has already been found to be globally useful are also noted.

How reliable are integral equations for the pair structure of binary fluid mixtures?

A recent thermodynamically self-consistent integral equation for the pair structure of simple fluids is solved for binary mixtures of “soft spheres” and compared to recent molecular dynamics results; excellent agreement is found.