Ground-state Kinetic Energy Research Articles

Electron momentum density and Compton profile by a semi-empirical approach

Here we propose a semi-empirical approach to describe with good accuracy the electron momentum densities and Compton profiles for a wide range of pure crystalline metals. In the present approach, we use an experimental Compton profile to fit an analytical expression for the momentum densities of the valence electrons. This expression is similar to a Fermi–Dirac distribution function with two parameters, one of which coincides with the ground state kinetic energy of the free-electron gas and the other resembles the electron–electron interaction energy. In the proposed scheme conduction electrons are neither completely free nor completely bound to the atomic nucleus. This procedure allows us to include correlation effects.We tested the approach for all metals with Z=3–50 and showed the results for three representative elements: Li, Be and Al from high-resolution experiments.

Properties of the Ut 2-electrons in two dimensions using the hubbard model

We examine the behaviour of 2 electrons on a 2 x 2 square lattice sites. The Hubbard model was used to model the system and was diagonalized using the configuration interaction method which is a variational method. The variations of the ground state energy ground state double occupied sites D, and the ground state kinetic energy with the interaction strength (u 0) were examined. The functions and were found to be parabolic functions of. This suggests that superconductivity is driven by both electron and hole doping. Key words: Hubbard model, Superconductivity, Configuration interaction and Electron correlation.

Electron mobility in dense argon gas at several temperatures

The mobility /spl mu/ of excess electrons in dense Argon gas was measured as a function of the applied electric field E and of the gas density N at several temperatures in the range 142.6 T/sub c/, shows the well known anomalous positive density effect, i.e., /spl mu//sub 0/N increases with increasing N. Below T,, however, /spl mu//sub 0/N does not show the expected effect, but features a broad maximum. This appears to be a crossover behavior between the positive density effect shown for T > T, and the small negative effect previously observed for T /spl ap/ 90 K However, the data at all temperatures confirm the interpretation of the anomalous density effect as being essentially due by the density-dependent quantum shift of the electron ground state kinetic energy in a disordered medium as a result of multiple scattering (MS) processes, although other MS processes influence the experimental outcome.

Neutron measurements of the single-particle kinetic energies in solid neon

Direct measurements of the mean atomic kinetic energy of solid neon have been made at 16 temperatures in the range 5--22 K and saturated vapor pressure. The measurements were made at high momentum and energy transfers using the technique of neutron Compton scattering. These extensive data have been compared with published calculations, and there is general agreement. The ground-state kinetic energy in condensed neon has been determined to be 41(2) K.

Lowering of the kinetic energy in interacting quantum systems.

Interactions never lower the ground state kinetic energy of a quantum system below the noninteracting value. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy. This can be demonstrated from a first order weak coupling expansion. Simulations (both variational and restricted path integral Monte Carlo) of the electron gas model and dense hydrogen confirm this and show that in contrast to the ground state case, at nonzero temperature the population of low momentum states can be increased relative to the free Fermi distribution. This effect is not seen in simulations of liquid 3He.

Direct measurements and path integral Monte Carlo calculations of kinetic energies of solid neon

Direct measurements are reported of the kinetic energies of FCC neon at seven temperatures between 4.25 and 20.2 K. The measurements employed the electronvolt spectrometer which is the neutron scattering instrument at the ISIS neutron source, UK. Wavevector transfers Q from 306 to were used, far larger than previously, in a regime where possible final-state-effect corrections to the observed longitudinal neutron Compton profile J(y) are easily deal with by a simple correctional procedure. The results are of comparable precision with the best previous work, carried out using the HRMECS instrument at IPNS, Argonne. From those previous measurements, Peek et al give a ground-state kinetic energy of . Path-integral Monte Carlo calculations were performed using both HFD-C2 and Lennard-Jones pair potentials. At 4.13 K, 10.13 K, 15.69 K and 20.31 K the HFD results were , , and , respectively. These values are broadly in agreement with the current measurements. They are significantly lower than the published values obtained from an HFD-based Wigner - Kirkwood high-temperature expansion including terms up to .

FERMION-SPIN APPROACH TO STUDY A DOPED ANTIFERROMAGNET

Within the mean-field approximation, we discuss effects of the projection operator in the fermion-spin theory. The ground-state kinetic energy of the t-J model is studied, and the results show that the mean-field ground-state kinetic energy is consistent with the numerical results. The possible phase separation is also discussed.

KINETIC ENERGY AND PHASE SEPARATION IN A DOPED ANTIFERROMAGNET

The ground-state kinetic energy of the t-J model is studied within the mean field approximation by using the fermion-spin transformation, the results show that the mean field ground-state kinetic energy is close to the numerical result at under dopings, and roughly consistent with the numerical result at optimal dopings. It is also shown that the frustration term J′ is favourable to diminish the range of the phase seperation in the t-J model.

Response function of the t-J model calculated using anyon techniques.

We have computed zero-temperature properties of the t-J Hamiltonian using the formalism of anyon superconductivity. The results of these calculations agree quantitatively with exact-diagonalization studies. These properties include the optical conductivity, the ground-state kinetic energy, and the ground-state magnetic energy. Implicit in this calculational procedure is a Kosterlitz-Thouless transition temperature for the onset of superconductivity.

Single-particle kinetic energies in solid neon.

Inelastic-eV-neutron-scattering experiments have been performed on solid natural neon at five temperatures between 4.7 and 26.4 K and at pressures between equilibrium vapor pressure and 17.6 MPa. Measurements of atomic-recoil line broadening were made within the impulse approximation. Average single-particle kinetic energies 〈${\mathit{E}}_{\mathit{k}}$〉 have been obtained by assuming a Gaussian atomic momentum distribution. A ground-state kinetic-energy value of 49.1\ifmmode\pm\else\textpm\fi{}2.8 K is found and the temperature variation of 〈${\mathit{E}}_{\mathit{k}}$〉 is determined. Comparisons are made to somewhat restricted deductions of 〈${\mathit{E}}_{\mathit{k}}$〉 from previous experiments on neutron-phonon scattering and heat capacity. Comparisons with existing theoretical calculations show that none of them predicts the observed ground-state kinetic energy, although cell-model variational calculations and self-consistent harmonic calculations in the literature find that the ground-state kinetic energy is substantially larger than the ground-state potential energy, in agreement with our results.

Quantum mechanics and phase transitions in small noble-gas clusters

The quantum-statistical properties of Argon clusters are calculated applying a Path-Integral Monte-Carlo (PIMC) method. Results for pair correlation functions and kinetic-and configurational energy expectations for various cluster sizes and temperatures are presented. Physical phenomena such as ground-state kinetic energy and quantum admixture of different atomic configurations are studied and experiences with the method are given. In particular, the relation between metastable cluster states and phase transitions is discussed.

Some tests of an approximate density functional for the ground-state kinetic energy of a fermion system.

Any proposed approximation to the ground-state kinetic energy of a system of noninteracting fermions in terms of the particle density \ensuremath{\rho}(r) can be used to estimate the potential field v(r) that will give rise to a given \ensuremath{\rho}(r), or the \ensuremath{\rho}(r) that will result from placing a given number of particles in a given v(r). Comparison with exact quantum-mechanical calculations thus gives two possible types of tests for any proposed kinetic-energy functional. This paper reports such tests for a recently proposed nonlocal functional applicable to one-dimensional systems, comparing its predictions for several simple problems not only with the correct answers but also with the predictions of Thomas-Fermi and Thomas-Fermi-Weizs\"acker functionals, to which the new functional proves considerably superior. The comparisons yield useful insights on the virtues and defects of the new functional, and on the directions in which improvements should be sought. Particular attention is devoted to Friedel oscillations and shell structure. It is shown that functionals of the Thomas-Fermi-Weizs\"acker type can never predict multiple maxima in \ensuremath{\rho} if v has only a single minimum and no maxima; the new functional does not have this defect, though it yields density oscillations rather weaker than the exact quantum-mechanical calculations. A natural general inference from the present tests is that any satisfactory kinetic-energy functional must (as ours does) replace the entire Thomas-Fermi term by a nonlocal expression.

Comparative study of the gradient expansion of the atomic kinetic energy functional-neutral atoms

In a previous work, it has been shown that for the noble gas atoms, the ground state kinetic energy functional T[ρ], where ρ is the electronic density, can be computed to surprising accuracy from the truncated gradient expansion: T[ρ]=T0[ρ]+T2[ρ]+T4[ρ], with T0[ρ] =3/10(3π2) ℱρ5/3dτ, T2[ρ]=1/72ℱ (∇ρ)2/ρdτ, and T4[ρ] given by the formula of Hodges. In this work, we report systematic calculations for improved near-Hartree–Fock atomic densities up to Z=54. We find that the truncated gradient expansion of T[ρ] can also lead to very good kinetic energies for open-shell and unpaired-electron atoms. The value given by T[ρHF] generally gets better, as compared with the Hartree–Fock result, as Z increases. For the Xe atom, T0+T2+T4 is within 0.08% of the exact Hartree–Fock kinetic energy with T2/T0=0.048, T4/T2=0.16. It is interesting to note that some minima appear in the deviation curves for T0, T0+T2, and T0+T2+T4, as compared with Hartree–Fock results. For the near-degenerate ground and lower excited states of some atoms, the truncated kinetic energy expansion can reproduce the relative kinetic energies qualitatively. On the other hand, because the cusp condition at the atomic nucleus and the exponentially vanishing density are valid for every Hartree–Fock density, it may not be possible to reproduce the Hartree–Fock or exact results with the gradient expansion in a systematic way.

Spin and uncertainty in the interpretation of quantum mechanics

A rigorous derivation of the Schrödinger theory from the Pauli (or Dirac) theory implies that the Schrödinger equation describes an electron in an eigenstate of spin. Furthermore, the ground-state kinetic energy is completely determined by the electron spin density. This can be explained by interpreting the spin as an orbital angular momentum, which is necessarily accompanied by a kinetic energy. Thus, the spin is a zero-point angular momentum associated with the zero-point energy of the electron. Since the dispersion in electron momentum is determined by the zero-point energy, the Heisenberg uncertainty relations for an electron can be interpreted as a property of the electronspin motion. The kinetic interpretation of spin and the statistical interpretation of quantum mechanics can be jointly sustained by regarding the electron as a point particle. It follows that stationary electron states are sources of fluctuating electric fields. There is reason to believe that these fluctuating fields are responsible for the Van der Waals force and can be identified with electromagnetic vacuum field fluctuations. The kinetic interpretation of spin then implies that the Van der Waals forces are spin dependent. These ideas are not only consistent with the conventional mathematical formalism of quantum mechanics, they provide a more complete and coherent interpretation of many details in the formalism than does the alternative Copenhagen interpretation. They present some difficulties, however, which, if the kinetic interpretation of spin is correct, probably require some modification of quantum electrodynamics to be resolved.