Stability of atoms and molecules in an ultrarelativistic Thomas-Fermi-Weizsaecker model

We consider the zero mass limit of a relativistic Thomas-Fermi-Weizsaecker model of atoms and molecules. We find bounds for the critical nuclear charges that ensure stability.Comment: 8 pages, LaTe

Quantum Field Theory in the Large N Limit: a review

We review the solutions of O(N) and U(N) quantum field theories in the large $N$ limit and as 1/N expansions, in the case of vector representations. Since invariant composite fields have small fluctuations for large $N$, the method relies on constructing effective field theories for composite fields after integration over the original degrees of freedom. We first solve a general scalar U(\phib^2) field theory for $N$ large and discuss various non-perturbative physical issues such as critical behaviour. We show how large $N$ results can also be obtained from variational calculations.We illustrate these ideas by showing that the large $N$ expansion allows to relate the (\phib^2)^2 theory and the non-linear $\sigma$-model, models which are renormalizable in different dimensions. Similarly, a relation between $CP(N-1)$ and abelian Higgs models is exhibited. Large $N$ techniques also allow solving self-interacting fermion models. A relation between the Gross--Neveu, a theory with a four-fermi self-interaction, and a Yukawa-type theory renormalizable in four dimensions then follows. We discuss dissipative dynamics, which is relevant to the approach to equilibrium, and which in some formulation exhibits quantum mechanics supersymmetry. This also serves as an introduction to the study of the 3D supersymmetric quantum field theory. Large $N$ methods are useful in problems that involve a crossover between different dimensions. We thus briefly discuss finite size effects, finite temperature scalar and supersymmetric field theories. We also use large $N$ methods to investigate the weakly interacting Bose gas. The solution of the general scalar U(\phib^2) field theory is then applied to other issues like tricritical behaviour and double scaling limit.Comment: Review paper: 200 pages, 13 figure

Libxc: a library of exchange and correlation functionals for density functional theory

The central quantity of density functional theory is the so-called exchange-correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of the theory. For the past 50 years, hundreds of such approximations have appeared, with many successfully persisting in the electronic structure community and literature. Here, we present a library that contains routines to evaluate many of these functionals (around 180) and their derivatives.Comment: 15 page

Thomas-Fermi Calculation of the Interlayer Force in Graphite

A model of a graphite crystal is proposed in which planar layers of positive charge are considered instead of the point charges of nuclei. The interlayer electronic density is calculated integrating both the Thomas-Fermi and the Thomas-Fermi-Dirac equations. From these densities, the total energy of the electrons is calculated including corrections for inhomogeneity in the form of Weizsäcker and Kirzhnits. The influence of the different corrections is studied with the result that the best method is to calculate the density from the Thomas-Fermi-Dirac equation and to take into account the inhomogeneity corrections in the form of Kirzhnits