Liquid-vapour coexistence of molecular fluids

We derive, for a liquid-vapour system with pairwise interactions, an infinite set of sum rules relating the pressure and temperature to integrals over the density profile and pair correlation function. For approximate forms for the variation of the pair correlation function through the liquid-vapour interface, these sum rules reduce to equations describing the coexistence curve of the fluid. Good agreement with experiment is obtained for all fluids considered.     

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.     

Charge and Current Sum Rules in Quantum Media Coupled to Radiation II

This paper is a continuation of the previous study (Šamaj in J. Stat. Phys. 137:1–17, 2009), where a sequence of sum rules for the equilibrium charge and current density correlation functions in an infinite (bulk) quantum media coupled to the radiation was derived by using Rytov’s fluctuational electrodynamics. Here, we extend the previous results to inhomogeneous situations, in particular to the three-dimensional interface geometry of two joint semi-infinite media. The sum rules derived for the charge-charge density correlations represent a generalization of the previous ones, related to the interface dipole moment and to the long-ranged tail of the surface charge density correlation function along the interface of a conductor in contact with an inert (not fluctuating) dielectric wall, to two fluctuating semi-infinite media of any kind. The charge-current and current-current sum rules obtained here are, to our knowledge, new. The current-current sum rules indicate a breaking of the directional invariance of the diagonal current-current correlations by the interface. The sum rules are expressed explicitly in the classical high-temperature limit (the static case) and for the jellium model (the time-dependent case).     

Ultrasoft contribution to heavy-quark pair production near threshold

We compute the third-order correction to the heavy-quark current correlation function due to the emission and absorption of an ultrasoft gluon. Our result supplies a missing contribution to top-quark pair production near threshold and the determination of the bottom quark mass from QCD sum rules.     

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension condensates containing at least one pair. We extract the direct single-instanton contribution to the sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel. Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998     

Decay of correlations and related sum rules in a layered classical plasma

Summary The asymptotic behaviours of particle correlation functions and the related sum rules are discussed for a layered classical plasma withe ²/r interactions in the fluid state, in dependence on the number of layers. These properties derive from consistency conditions imposed by screening on the hierarchical equations, as already treated by A. Alastuey and P. A. Martin (J. Stat. Phys.,39, 405 (1985)) for various Coulomb fluids. The main results concern i) the type of clustering of correlations needed for the validity of multipolar sum rules at various orders, ii) the proof that the pair correlation function in a finite multilayer may carry an electric dipole moment and the calculation of its partioning among the layers, and iii) the dimensionality crossover in an infinitely extended or periodically repeated multiplayer with varying interlayer spacing and wave vector.     

Effect of structural considerations on the development of free energy functionals for the square-well fluid

ABSTRACT

In this work, we compare four inhomogeneous square-well fluid models, only distinct in the approximation on the pair correlation function present in the attractive free energy term of the density functional theory (DFT). Various criteria can be considered to select or validate an approximation, depending on fundamental interests or for a specified application. Here the considered criteria of selection were the verification of sum rules, and the prediction of both the adsorbed quantity and the density profiles. Even if a model satisfies one of these criteria, it may fail to describe others, so they can be considered supplementary to each other and in no case redundant. According to this study, one can attach more importance to any of these criteria depending on the specific objectives intended for the model development and purpose. They can serve as references in the development of new DFT models, eventually with other criteria, according to the objective of the work and the accuracy desired.     

W boson pair production by electrons and positrons of same helicity

TheW boson pair production by electron and positron of same helicity is computed. The restrictions due to the tree unitarity are exhibited in three sum rules and we have shown how the gauge theories satisfy the sum rules. A simple way to isolate heavy lepton contributions is presented.     

Neutron diffraction experiments on a fluid,equimolar mixture of methane and carbon tetrafluoride

A neutron scattering investigation is reported on an equimolar mixture of methane and carbon tetrafluoride along the 370 K isotherm for four different thermodynamic states in a pressure range 270–800 bar, the aim of which was to provide more structural data about this non-ideal system. The fully corrected coherent differential cross-section is presented. The weighted sum of the total atom pair correlation functions is separated into the intramolecular and intermolecular contributions and the structural parameters of the molecules in the fluid state are determined. The density dependence of the intermolecular atom pair correlation functions is clearly visible. The experimental results are compared with previous experiments on the pure components and XRISM calculations, based on a one-centre Lennard-Jones potential.     

Exact sum rules for inhomogeneous drums

We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one dimensional inhomogeneous systems that we have obtained in a previous paper. We also discuss the extension of these formulas to higher dimensions. We show that in the special case of a density depending only on one variable the sum rules of any integer order can be expressed in terms of a single series. As an application of our result we derive exact sum rules for the homogeneous circular annulus with different boundary conditions, for a homogeneous circular sector and for a radially inhomogeneous circular annulus with Dirichlet boundary conditions.     

Sum rules for X-ray magnetic circular dichroism spectra in strongly correlated ferromagnets

It is proven that the sum rules for X-ray magnetic dichroism (XMCD) spectra that are used to separate spin and orbital contributions to the magnetic moment are formally correct for an arbitrary strength of electron-electron interactions. However, their practical application for strongly correlated systems can become complicated due to the spectral density weight spreading over a broad energy interval. Relevance of incoherent spectral density for the XMCD sum rules is illustrated by a simple model of a ferromagnet with orbital degrees of freedom.     

Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

Skyrme liquid versus Skyrme solid

Based on generic sum rules for two-dimensional, isotropic electron quantum liquids in the lowest Landau level, we propose analytic pair distribution functions for spin-polarized and spin-unpolarized liquid phases at filling factors . From the pair distribution functions we calculate the energy of such liquid phases and compare with the energy of the solid phase. The comparison suggests that the quantum melting phase transition to the Skyrme solid may lie much closer to ν=1 than ever expected.     

The Explicit Density Functional and Its Connection with Entropy Maximization

The intrinsic Helmholtz free energy, commonly used as a basis for density functional theories, is here given explicitly as a cluster diagram expansion with density field points. Also given are explicit variational procedures for determining the chemical potential for a given density, the pair potential for a given pair correlation function, and the pair correlation function for a given pair potential. The physical meaning of the density functional is established within the context of a new derivation of statistical mechanics based on entropy that supplies a variational principle for equilibrium by generalizing the thermodynamic potential to nonequlibrium states. This shows that the conventional density functional determines not only the equilibrium density, but also the probability of fluctuations about that density.     

New approach to axial coupling constants in the QCD sum rule

We derive new QCD sum rules for the axial coupling constants by considering the correlation functions of axial-vector currents in a one-nucleon state. The QCD sum rules tell us that the axial coupling constants are expressed by nucleon matrix elements of quark-gluon composite operators which are related to the sigma terms and the moments of parton distributions. The results for the isovector axial coupling constants and the eighth component of the SU(3)(f) octet are in good agreement with experiment.     

Structural and electronic properties of Danzer's model of a three-dimensional quasicrystal

By using deflation rules, the coordinates of the atoms in Danzer's model of a 3d quasicrystal are computed. The resulting atomic positions in a cut through the model well agree with experimental findings. Furthermore, for Danzer's model the static structure factor, the pair correlation function, and properties of a tight binding electron model are studied. The electron density of states shows a characteristic peak at energyE=O, which may be associated to confined states.     

Current correlation functions,QCD sum rules and vector mesons in baryonic matter

Based on an effective Lagrangian which combines chiral SU(3) dynamics with vector meson dominance, we have developed a model for the forward vector meson-nucleon scattering amplitudes. We use this as an input to calculate the low energy part of the current-current correlation function in nuclear matter. Its spectrum enters directly in the “left-hand side” of QCD sum rules. For the isovector channel we find a significant enhancement of the in-medium spectral density below the ϱ resonane while the ρ meson mass itself changes only slightly. The situation is different in the isoscalar channel, where the mass and peak position of the ω meson move downward while its width increases less drastically than in the ρ meson case. For the φ meson we find almost no mass shift; the width of the peak broadens moderately. We observe a remarkable degree of consistency with the operator product expansion of QCD sum rules in all three channels. We point out, however, that these results cannot simply be interpreted, as commonly done, in terms of a universal rescaling of vector meson masses in matter.     

Particle-hole asymmetry in doped mott insulators: implications for tunneling and photoemission spectroscopies

We use exact sum rules for the one-particle spectral function to quantify the idea that it is more difficult to add an electron than to extract one in a system with strong local repulsion. Our results explain the striking asymmetry in the tunneling spectra of underdoped cuprates which increases with underdoping. We also propose a novel method, based on ratios of sum rules, to estimate local density variations in inhomogeneous materials. Using a variational approach, we show that the origin of the particle-hole asymmetry lies in the incoherent spectral weight.     

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion,sum rules and the maximum entropy method

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.     

Longitudinal and bulk viscosities of binary fluid mixtures

Expressions for zeroth, second and fourth sum rules of longitudinal and bulk stress auto correlation functions have been derived for binary fluid mixtures. Longitudinal and bulk viscosities of an Ar–Kr mixture have been calculated using Mori's memory function formalism coupled with the sum rules of longitudinal and bulk stress auto correlation functions. The results obtained are compared with the molecular dynamics simulation. Mass dependence of the longitudinal and bulk viscosities has been studied for different compositions of an isotopic mixture at different densities and temperatures. For very large mass ratio, the longitudinal and bulk viscosities of the isotopic mixture are more dependent on mole fraction than on mass.