Gradient expansion of the Coulomb exchange energy

With the aid of the gradient expansion technique of Kirzhnits we calculate the lowest order inhomogenity correction to the local approximation of the Coulomb exchange energy density.     

Relativistic gradient expansion of the kinetic energy density

A systematic derivation of a relativistic inhomogeneity correction to the kinetic energy is given on the basis of the gradient expansion technique and the Foldy-Wouthuysen representation.     

Conversion between kinetic energy and potential energy in the classical nonlocal Boltzmann equation

An important property of the classical Boltzmann equation is that kinetic energy is conserved. This is closely connected to the fact that the Boltzmann equation describes the nonequilibrium properties of an ideal gas. Generalizations of the Boltzmann equation to higher density involve, among other things, allowing the colliding particles to be at different positions. This spatial nonlocality is known to contribute to the density corrections of gas transport properties. For soft potentials such a spatial separation of the particles also leads to a conversion between kinetic and potential energy. In evaluating these effects the classical dynamics of the whole collision trajectory must be taken into account, involving also the time for the collision process. The resulting time nonlocality has usually been reinterpreted in terms of a spatial nonlocality. However, for a homogeneous system this is not possible and only the time nonlocality remains, this then being responsible for the conversion between kinetic and potential energy. This paper aims to clarify these properties of the nonlocal corrections to the classical mechanical Boltzmann collision term. Comments on the corresponding problem for the quantum Boltzmann equation are also made.     

Study of some surface properties using a simple gradient expansion of the kinetic energy density functional

Summary Reasonable surface energies and very accurate surface dipole barrier and work function for a semi-infinite jellium are calculated from a simple model of the density. The model was proposed by Smith and contains one universal parameter. In the Kohn-Sham energy functional, the kinetic energy is approximated by its simple gradient expansion including a fourth-order term. The exchange and correlation are treated within the local-density approximation. Using the simple gradient, the energy is minimized with respect to the universal parameter of the density. The parameter which minimizes the energy is used to calculate the surface dipole barrier and the work function. A comparison was made with the Lang and Kohn results and with the Ma and Sahni results.     

A new expansion of kinetic equations

A small expansion parameter is investigated which is useful in cases where the dependence of average values of slowly-varying variables on the initial conditions is very small for the long time scale.     

Constrained minima of nonlocal free energy functionals

We consider variational problems involving nonlocal free energy functionals that arise from Gibbs measures with Kac potentials and are related to the characterization of the optimal (i.e., typical) shape of an interface under given constraints on the magnetization profile.     

Calculation of ground state surface properties of simple metals including non-local effects of the exchange and correlation energy

The energy density functional formalism is used to calculate the ground state surface energies and work functions for simple metals. Non-local corrections to the exchange and correlation energies were included by means of a gradient expansion in the density. Good agreement is obtained with experiment.     

Precursor of a plasma wave due to nonlocal kinetic phenomena

The propagation of a finite amplitude quasi-monochromatic wave packet in a plasma gives rise to a a particular incoherent precursor of the wave due to nonlinear kinetic effects if the velocity of resonant electrons is greater than the wave group velocity.     

Long-range electrostatic contributions to the many-body expansion of molecular potentials

A new approach is proposed to the introduction of long range electrostatic terms in the many-body expansion of the molecular potential. The method has been applied to the HO₂ and H₂F₂ potentials.     

Non-spherical contributions to the vacancy formation energy

A linear response formalism is presented which allows the calculation of the non-spherically symmetric (angular momentum index, l ≠ 0) response to a random external charge perturbation when the spherically symmetric response is available. This procedure is applied to the problem of the energy of vacancy formation so that the electron charge depletion in the vicinity of vacancy is taken into account. The non-spherical contribution to the energy formation for the alkali metals is estimated and found to be non-negligible.     

Third-order contributions to the binding energy of oxygen

Binding energy calculations reported in earlier papers using matrix elements deduced from phase shifts are continued to third order in a perturbative treatment. The total third-order contribution is small due to a cancellation between diagrams and there are indications that higher order terms are also small.     

Thermal expansion and kinetic coefficients of crystals

Electrical (ρ) and thermal (W) resistivities and thermal expansion coefficient (β) of Cu, Zn, Al, Pb, Ni, β-brass, Al₂O₃, NaCl, Si, SiO₂(∥), and SiO₂(⊥) were simultaneously measured with standard four-probe, absolute steady-state, and quartz dilatometer techniques. Measurements of Ni and β-brass were performed at temperatures from 300 to 1100 K and measurements of all other samples were made between 90 and 500 K. This temperature range includes the range below and above the Debye temperature (T_D). The total uncertainties of the specific electrical and thermal resistivities and thermal expansion coefficient (TEC) measurements are 0.5%, 3.0%, and (1.5-4.0%), respectively. The universal linear relationship between the electrical and thermal resistivities and βΤ over the wide temperature range was found experimentally. Using the Landau criterion for convection development for ideal phonon and electron gases in the solids, the universal relations, ρ^ph/ρ^*≡βT and W^ph/W^*≡βT (where ρ^ph is the phonon electrical resistivity, is the characteristic electrical resistivity, W^ph is the phonon thermal resistivity, and W^*=k_BG/qc_p is the characteristic thermal resistivity) between relative phonon electrical and phonon thermal resistivities and βΤ were derived. The derived universal relations provide a new method for estimating the kinetic coefficients (electrical and thermal resistivities) from TEC measurements.     

The expansion of the Fokker-Planck equation including a critical point

The known expansion of the master equation for weak diffusion in an external potential applies to both the monostable and the bistable case, but fails at the critical point. This can be remedied by taking as zeroth order approximation a suitably defined set of eigenfunctions. The resulting expansion is uniformly valid in a range of the pump parameter including the critical point.