Short-ranged correlations and the ferromagnetic electron gas

We give a complete analysis of covariant measurements on two spins. We consider the cases of two parallel and two antiparallel spins, and we consider both collective measurements on the two spins and measurements that require only local quantum operations and classical communication (LOCC). In all cases we obtain the optimal measurements for arbitrary fidelities. In particular, we show that if the aim is to determine as accurately as possible the direction in which the spins are pointing, it is best to carry out measurements on antiparallel spins (as already shown by Gisin and Popescu), second best to carry out measurements on parallel spins, and worst to be restricted to LOCC measurements. If the aim is to determine as accurately as possible a direction orthogonal to that in which the spins are pointing, it is best to carry out measurements on parallel spins, whereas measurements on antiparallel spins and LOCC measurements are both less suitable but equivalent.

Short-range correlation in electron gas

The effect of particle correlations in a classical system of charged particles moving in a static uniform background is investigated by means of a dielectric theory developed by Singwi et al. for a completely degenerate electron gas. In this theory, the short-range correlations arising from the Coulomb interaction is taken into account through a local-field correction depending on the pair correlation function. In a first approximation (I), the pair correlation function is chosen to be time independent. The extension of allowing also the pair correlation function to adjust itself to the external field results in a screening of the Coulomb potential entering the local field. The effect of this screening has been investigated for the cases of a static random-phase-approximation (RPA) dielectric function (II) and a static fully self-consistent dielectric function (III). Numerical self-consistent calculations have been carried out for the cases I-III in order to determine the static structure factor $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$. From $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ thus obtained, the Helmholtz free energy, the correlation energy, the pair correlation functions, and the isothermal compressibility have been calculated numerically, The plasma dispersion and the compressibility sum rule have also been investigated. The present method can be regarded as a rather natural extension of the RPA. Considerable improvement upon the simple Debye-H\"uckel (or, equivalently, classical RPA) is also found. The results of the present calculations are also compared with the results of other elaborate methods.

In this paper we show that a massive composite particle with spin zero can be a vector particle. If a massive particle is composed of a fermion and an antifermion with antiparallel spins and they are bound by a local interaction of the form , its field is a four-vector. We show that this composite particle with antiparallel spins cannot be transformed into a composite particle with parallel spins. If the pion or kaon is such a particle, this would explain how it can have spin 0 but still contain directional information as some experimental evidence indicates.

We present a systematic analysis of the nuclear two- and three-body short-range correlations and their relations to the zero-energy eigenstates of the Schr\"odinger equation. To this end we analyze the doublet and triplet coupled-cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these coupled-cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear two-body short range correlations, and they might also be helpful for general coupled-cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

We show that the defects of graphene, which lead to the non-equality between positive curvature of fermions with anti-parallel spins and negative curvature of fermions with parallel spins, imply an emergence of F(R) gravity. By increasing the number of atoms at each defect, the order of scalar curvature increases and the shape of F(R) gravity changes. This gravity has a direct relation with energy-momentum tensor and leads to motion of electrons in a special path and hence producing superconductivity. Also, for some special angles, parallel spins become close to each other and repel to each other. In that condition, the shape of F(R) gravity changes and electrons can't continue to move in an initial path and return. Consequently, superconductivity disappears and one new conductivity appears in opposite direction.

Inhomogeneous correlation functions for model ‘ soft’ 2–2 and 1–1 electrolytes at a charged interface have been determined by the so–called ‘pair’ approximation of integral equation theory. The solvent is modeled as a structureless dielectric continuum at 25°C. The wall–ion–ion structure is calculated using the inhomogeneous Ornstein–Zernike relation, together with the hypernetted chain closure, and one of two choices for the functional relationship between the singlet and pair correlation functions. Both the interfacial density profiles and the inhomogeneous pair correlation functions are calculated. For most cases, the inhomogeneous pair correlation functions near the interface vary significantly from the homogeneous pair correlation functions. This deviation generally becomes stronger as the charge on the surface increases, and the deviation generally extends out further from the interface as the surface charge increases. The density profiles predicted by the pair approximations generally show less structure than the singlet approximation density profiles, whereas the inhomogeneous pair correlation functions generally predict more structure than would be expected by simply assuming bulk pair correlation functions. The density profiles and inhomogeneous correlation functions are also found to agree qualitatively with previous simulations which used ‘charged hard–sphere/charged hard—wall’ potentials.

In no wave function of the type (1) [product of single determinants for each spin] is there a statistical correlation between the positions of the electrons with antiparallel spin. The purpose of the aforementioned generalization of (1) is to allow for such correlations. This will lead to an improvement of the wave function and, therefore, to a lowering of the energy value. E. Wigner, Phys. Rev. 46, 1002 (1934) Summary Although the exact many-body wavefunction cannot be written down in general, we do know of some of its properties. For example, there are differences between the wavefunctions of insulators and metals and the cusp condition gives the behavior as any two charges approach each other. In this chapter we also discuss approximate wavefunctions, ways to judge their accuracy and how to include electronic correlation. Examples of many-body wavefunctions are the Slater–Jastrow (pair product) wavefunction and its generalization to pairing and backflow wavefunctions. In other places in this book, we argue that it is not necessary to look at the many-body wavefunctions explicitly because they are unwieldy; the one- and two-body correlation functions discussed in Ch. 5 are sufficient to determine the energy and give information on the excitation spectra. However, these correlation functions do not always contain all information of interest. In principle, the ground-state energy of a many-electron system is a functional of the density, but the very derivation of the theorem invokes the many-body wavefunction, as expressed explicitly in Eq. (4.16). The effects of antisymmetry are manifest in the correlation functions, but antisymmetry is most simply viewed as a property of the wavefunction; electronic correlation is fundamentally a result of properties of the many-body wavefunction. Studying many-body wavefunctions provides a very useful, different point of view of many-body physics from the approaches based on correlation functions. Many of the most important discoveries in physics have come about by understanding the nature of wavefunctions, such as the Laughlin wavefunction for the fractional quantum Hall effect, the BCS wavefunction for superconductors, p-wave pairing in superfluid 3 He, and the Heitler– London approach for molecular binding. The role of Berry's phases has brought out the importance of the phase of the wavefunction in determining properties of quantum systems. This has led to new understanding of the classification of insulators, metals, superconductors, vortices, and other states of condensed matter.

Previous developments in the theory of metals may be divided clearly into two parts: that based principally upon the hypothesis of free electrons and dealing with conductivity properties, and that based upon calculations of valence forces and dealing with the chemical properties. In the present article an intermediate point of view is adopted and the free-electron picture is employed in an investigation of chemical properties of metallic sodium. The assumption is made that in the metal the $K$ and $L$ shells of an atom are not altered from their form in the free atom. The properties of the wave functions of the electrons are discussed qualitatively, first of all, and it is concluded that the binding energy will be positive even when the Pauli principle is taken account of. This is followed by a quantitative investigation of the energy to be associated with the lowest state. First of all it is shown to what extent the present picture takes account of the interactions of electrons with both parallel and antiparallel spins, and to what extent remaining effects may be neglected. Next a Schroedinger equation is solved in order to determine the lowest energy level for various values of the lattice constant. To this a correction is made to account for the Pauli principle and from the result the lattice constant, binding energy and compressibility are calculated with favorable results.

The model in which positive ions in a metal are smeared into a uniform neutralizing background in which interacting electrons move is first considered at some length, especially rather near to the metal-insulator (Wiper) transition. Properties considered carefully are (a) the electronic momentum distribution as a function of background density, and (b) the pair correlation function. Features connected with both the long-range Coulombic repulsion and the transition from delocalized to localized behaviour will be highlighted in terms of (a) and (b) above. The possible use of this model as a reference state against which to consider the alkali metals, in both normal and expanded form, will then be discussed. In Na, the importance of 3s–3p hybridization will be emphasized, the Heisenberg model providing a surprisingly useful account of some bulk properties. Diffraction evidence on the degenerate electron assembly in molten Na and K will be considered in support of pronounced metallic bonding. Expanded Cs along the coexistence curve will next be treated, especially the observed magnetic susceptibility which changes from Fermi liquid behaviour to Curie-Weiss form as the critical point is approached. The crossover point is discussed in terms of heavy fermion theory and is shown to contain information about the discontinuity of the electronic momentum distribution at the Fermi surface. This discontinuity is much smaller than that in jellium (the smeared ion model above) and testifies to the importance of the electron-ion interaction at this density, which cannot be treated perturbatively. Finally, the possibility of the co-existence of molecules in metallic phases is considered, with particular reference to metallic hydrogen and metallic iodine near the metal-insulator transition. For the latter, experimental evidence can leave little doubt that there is at least a limited range of pressures over which the metallic ground state of iodine contains I2 molecules, and some discussion of this strongly correlated state will be included.

We have measured the difference between the pp total cross sections for parallel and antiparallel longitudinal spin states at beam momenta of 2.75, 2.92, 3.25, and 3.48 GeV/c. These results reveal possible new structure in this momentum range.

Results on two-particle angular correlations for charged particles emitted in proton-proton collisions at center-of-mass energies of 0.9, 2.36, and 7 TeV are presented, using data collected with the CMS detector over a broad range of pseudorapidity (eta) and azimuthal angle (phi). Short-range correlations in Delta(eta), which are studied in minimum bias events, are characterized using a simple "independent cluster" parametrization in order to quantify their strength (cluster size) and their extent in eta (cluster decay width). Long-range azimuthal correlations are studied differentially as a function of charged particle multiplicity and particle transverse momentum using a 980 inverse nb data set at 7 TeV. In high multiplicity events, a pronounced structure emerges in the two-dimensional correlation function for particle pairs with intermediate transverse momentum of 1-3 GeV/c, 2.0< |Delta(eta)| <4.8 and Delta(phi) near 0. This is the first observation of such a long-range, near-side feature in two-particle correlation functions in pp or p p-bar collisions.

We report results for the electronic, structural and dynamical properties of liquid GaAs simulated by using ab initio molecular dynamics. Results for the total and partial structure factors, self-diffusion properties, pair correlation and angular distribution functions, and the electronic density of states are presented. Our calculated structure factor and pair correlation functions are in good agreement with available experimental data. A “common neighbor” cluster analysis is used to examine the structure of the liquid.

We evaluate imaginary time density-density correlation functions for two-dimensional homogeneous electron gases of up to 42 particles in the continuum using the phaseless auxiliary field quantum Monte Carlo method. We use periodic boundary conditions and up to 300 plane waves as basis set elements. We show that such methodology, once equipped with suitable numerical stabilization techniques necessary to deal with exponentials, products, and inversions of large matrices, gives access to the calculation of imaginary time correlation functions for medium-sized systems. We discuss the numerical stabilization techniques and the computational complexity of the methodology and we present the limitations related to the size of the systems on a quantitative basis. We perform the inverse Laplace transform of the obtained density-density correlation functions, assessing the ability of the phaseless auxiliary field quantum Monte Carlo method to evaluate dynamical properties of medium-sized homogeneous fermion systems.

An alternative approach to the quantum statistics of interacting particles is proposed. It consists of calculating the equilibrium thermodynamical quantities of the many-body system via the pair distribution function with the assumption that the particles interact with each other only through pair central forces. The proposed approach has some advantage over the usual treatment via the partition function in that the pair distribution function is easier to deal with than the partition function in certain circumstances particularly when the collective motion description of the system is desirable. This is because only the pair distribution function can be expressed directly in terms of the collective interaction which is closely connected with collective elementary excitation, such as a plasmon in the electron gas and a phonon in the hard-sphere Boson gas. The equation of state as well as the internal energy are obtained in the form of integrals of the pair distribution function. The close analogy between the pair distribution function and the two-body propagator, which appears in the quantum field theory, makes it possible to analyze the former by the use of Feynman diagrams identical with those usually introduced for the latter. The collective interaction, which is defined by the sum of the direct and the indirect interactions, is introduced as a particular partial sum of the perturbation series of the pair distribution function. This is used in rewriting the pair distribution function in terms of the collective interaction.It is shown that, while the simple chain approximation to the collective interaction in the electron gas is responsible for the transfer of a plasmon, the same approximation to the collective pseudo-interaction in the hard-sphere Boson system has a relation similar to that of transfer of a phonon, both cases occuring at low temperatures. The explicit calculation of the pair distribution functions for these systems at the absolute zero temperature is carried out up to the first order in the collective interaction (simple chain approximation.) These results are used to calculate the ground-state energies. For the electron gas the energy thus obtained confirms Gell-Mann-Bruckner's calculation of the correlation energy. For the hard-sphere Bosons the calculated energy reproduces the result of Lee, Huang, and Yang. The extension of the calculation to the finite temperature case is also indicated. In particular the classical Debye-Huckel equation of state for the electron gas is briefly discussed.