Particle Correlations in a Classical One-Component Plasma

We develop an equivalent of the Debye-Hückel weakly coupled equilibrium theory for layered classical charged particle systems composed of one single charged species. We consider the two most important configurations, the charged particle bilayer and the infinite superlattice. The approach is based on the link provided by the classical fluctuation-dissipation theorem between the random-phase approximation response functions and the Debye equilibrium pair correlation function. Layer-layer pair correlation functions, screened and polarization potentials, static structure functions, and static response functions are calculated. The importance of the perfect screening and compressibility sum rules in determining the overall behavior of the system, especially in the r--> infinity limit, is emphasized. The similarities and differences between the quasi-two-dimensional bilayer and the quasi-three-dimensional superlattice are highlighted. An unexpected behavior that emerges from the analysis is that the screened potential, the correlations, and the screening charges carried by the individual layers exhibit a marked nonmonotonic dependence on the layer separation.

We present a comprehensive study of plasmon dispersions in simple metals and Heusler compounds based on an accurate ab-initio evaluation of the momentum and frequency dependent dielectric function in the random-phase approximation. Using a momentum-dependent tetrahedron method for the computation of the dielectric function, we extract and analyze "full" and "intraband" plasmon dispersions: The "full" plasma dispersion is obtained by including all bands, the intraband plasma dispersion by including only intraband transitions. For the simple metals silver and alu- minum, we show that the intraband plasmon dispersion has an unexpected downward slope and is therefore markedly different from the results of an effective-mass electron-gas model and the full plasmon dispersion. For the two Heusler compounds Co2FeSi and Co2MnSi, we present spectra for the dielectric function, their loss functions and plasmon dispersions. The latter exhibit the same negative intraband plasmon dispersion as found in the simple metals. We also discuss the influence of spin-mixing on the plasmon dispersion.

We report angle-resolved Raman scattering observations of the temperature-dependent Landau damping of the acoustic plasmon in an electron bilayer system realized in a GaAs double-quantum-well structure. Corresponding calculations of the charge-density excitation spectrum of the electron bilayer using forms of the random-phase approximation (RPA), and the static local field formalism of Singwi, Tosi, Land and Sjölander (STLS) extended to incorporate non-zero electron temperature Te and phenomenological damping, are also presented. The STLS calculations include details of the temperature dependence of the intra- and inter-layer local field factors and pair correlation functions. Good agreement between experiment and the various theories is obtained for the acoustic plasmon energy and damping for Te TF/2, where TF is the Fermi temperature. However, contrary to current expectations, all of the calculations show significant departures from our experimental data for Te TF/2. From this, we go on to demonstrate unambiguously that real local field factors fail to provide a physically accurate description of exchange correlation behaviour in low-dimensional electron gases. Our results suggest instead that one must resort to a dynamical local field theory, characterized by a complex field factor to provide a more accurate description.

The dielectric property of an electron gas confined to the surface of the cylinder is investigated in the random phase approximation. The frequency dependence of the dielectric function shows a dimensional crossover from two- to one-dimensional behavior with decreasing the cylinder radius. In this model, the Fourier transform of the Coulomb potential is exactly performed. The plasma dispersion relation at long wavelengths is derived by considering the polarizability that comes from both intraband and interband transitions. It is shown that the intraband plasma dispersion agrees with that of the quantum wires. The dielectric function of the two-dimensional electron gas is also derived analytically from that of the electron gas on the cylinder surface.

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.

Quantized vortices in liquid 4He at finite temperatures are treated by first principles theory that extends results presented in paper I of this two-part set. Then the possible role of thermally excited quantized vortices in accounting for the λ transition is studied. This study indicates that vortices are probably not the dominant mechanism responsible for the λ transition, but that they may account for some minor effects near Tλ. A model that identifies critical fluctuations with quantized isothermal fourth sound waves is developed and used to derive formulas for specific heat in He II and He I. Logarithmic divergence of the constant volume specific heat is found. Numerical calculations using those formulas produce close agreement with experimental data. A formula for the radial distribution function near Tλ in He II and He I is derived and numerically evaluated. A formula for the correlation length is derived and numerically evaluated and physical characteristics of the correlation length are discussed. Numerical calculations based on that formula for correlation length are compared with experimental results. Long-range order in the liquid exhibited in the radial distribution function and correlation length is shown not to involve a Bose-Einstein condensate in this theory. The isothermal compressibility is found by integration of the radial distribution function and the result shows that isothermal compressibility is unchanged by critical fluctuations of isothermal fourth sound.

The fulfilment of sum rules for the loss function which is determined using different models of the dielectric function (DF): the random phase approximation (RPA), Mermin, and extended models of RPA and Mermin is investigated1. In the extended models the dynamic collision frequency is used, which is calculated according to computer simulations and within the Born-Mermin model. It is shown that the DF obtained by the method of moments satisfy all sum rules. For other models of DF these equalities hold in part. Mermin and RPA models do not satisfy known, associated with convergent frequency zero and fourth moment, sum rules, but satisfy the second sum rule. These models take into account the electron-electron interaction only with the introduction of electron correction on a local-field, but do not take into account the electron-ion interaction.

Unified SAFT-VR theory for simple and chain fluids formed of square-well, triangular-well, Sutherland and Mie segments

The setting up of relations between the radial distribution function and some thermodynamic quantities is continued in this chapter. That of interest, here, is the isothermal compressibility coefficient. During the course of the reasoning mentioned in this chapter, a new function is introduced. It is the function G which, in turn, is itself a function of the radial distribution function \( \overline{g} \)(R). The name of G is spatial pair correlation function or Kirkwood–Buff’s integral. Another relation, which relates the fluctuations of the numbers of molecules to the isothermal compressibility factor, is also set up. All these quantities are linked together. These relations are, actually, the starting theoretical basis of Kirkwood–Buff’s theory which is very interesting for the study of activities.

Theoretical calculations of the isothermal compressibility for simple fluids

The pair correlation function, the screening of a fixed impurity charge, the correlation energy, the cohesive energy of alkali metals, and the plasmon dispersion relation in the small-$k$ limit are calculated using an expression for the dielectric function derived in a previous paper. Results are compared with those obtained from other theories.

We discuss different methods of calculation of the screened Coulomb interaction $U$ in transition metals and compare the constraint local-density approximation (LDA) with the GW approach. We clarify that they offer complementary methods of treating the screening and should serve for different purposes. In the GW method, the renormalization of bare on-site Coulomb interactions between 3d electrons occurs mainly through the screening by the same 3d electrons, treated in the random phase approximation (RPA). The basic difference of the constraint-LDA method is that it deals with the neutral processes, where the Coulomb interactions are additionally screened by the ``excited'' electron, since it continues to stay in the system. This is the main channel of screening by the itinerant ($4sp$) electrons, which is especially strong in the case of transition metals and missing in the GW approach, although the details of this screening may be affected by additional approximations, which typically supplement these two methods. The major drawback of the conventional constraint-LDA method is that it does not allow to treat the energy-dependence of $U$. We propose a promising approximation based on the combination of these two methods. First, we take into account the screening of Coulomb interactions in the 3d-electron-line bands located near the Fermi level by the states from the subspace being orthogonal to these bands, using the constraint-LDA methods. The obtained interactions are further renormalized within the bands near the Fermi level in RPA. This allows the energy-dependent screening by electrons near the Fermi level including the same 3d electrons.

In the fractional dimensional space, the ground state properties of the charged-boson fluid are studied in a theory which goes beyond the random phase approximation by including correlations through a static local-field-factor. The structure factor and static local field-factor are obtained in the self-consistent method. Qualitative agreement with the Monte Carlo results on static screening is achieved by imposing self-consistency on the compressibility of the fluid in addition to self-consistency on the structure factor. Using the structure factors obtained in these methods, several properties of the charged boson system such as the energy spectrum of elementary excitations, the pair-correlation function, the ground state energy, the pressure, the chemical potential and the compressibility are obtained in several dimensions including both integer and fractional values. Results obtained in the later method in two and three dimensional systems are close to the Monte Carlo and hypernetted-chain methods. The Wigner crystallisation in the lower dimensional system is found at higher density of bosons. However, it vanishes in any lower dimensional system whose dimension lies below 2.

Optical properties can be determined by either the transverse dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q,\ensuremath{\omega}) or the longitudinal dielectric function ${\mathrm{\ensuremath{\epsilon}}}_{\mathcal{n}}$(q,\ensuremath{\omega}) in the long wavelength limit, i.e., q\ensuremath{\rightarrow}0. By expressing ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) in terms of density response functions, we calculate the third, fifth, and seventh frequency moments of Im${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) in addition to the first frequency moment, the well-known conductivity sum rule. While the third and fifth moments reflect the inhomogeneity of the system, correlation effects contribute explicitly to the seventh moment. In addition, the frequency moments of Im[-1/${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\parallel}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega})] can be constructed from these moments. The dielectric functions evaluated in a self-consistent field (SCF) approximation, such as the random phase approximation (RPA) or the adiabatic local density approximation (ALDA), satisfy the first three odd frequency moments provided the single particle states on which the SCF calculation is based are calculated in the corresponding SCF approximation. The seventh frequency moment constitutes a severe requirement that ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\perp}}}$(q\ensuremath{\rightarrow}0,\ensuremath{\omega}) evaluated in the RPA or the ALDA cannot satisfy. This is demonstrated for nearly free electron systems.

Infrared spectroscopy of solids