High-density correlation energy expansion of the one-dimensional uniform electron gas

We show that the expression of the high-density (i.e small-$r_s$) correlation energy per electron for the one-dimensional uniform electron gas can be obtained by conventional perturbation theory and is of the form \Ec(r_s) = -\pi^2/360 + 0.00845 r_s + ..., where $r_s$ is the average radius of an electron. Combining these new results with the low-density correlation energy expansion, we propose a local-density approximation correlation functional, which deviates by a maximum of 0.1 millihartree compared to the benchmark DMC calculations.Comment: 7 pages, 2 figures, 3 tables, accepted for publication in J. Chem. Phy

Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.Comment: 20 pages, 7 figures, calculation of Casimir energy adde

Long-range/short-range separation of the electron-electron interaction in density functional theory

By splitting the Coulomb interaction into long-range and short-range components, we decompose the energy of a quantum electronic system into long-range and short-range contributions. We show that the long-range part of the energy can be efficiently calculated by traditional wave function methods, while the short-range part can be handled by a density functional. The analysis of this functional with respect to the range of the associated interaction reveals that, in the limit of a very short-range interaction, the short-range exchange-correlation energy can be expressed as a simple local functional of the on-top pair density and its first derivatives. This provides an explanation for the accuracy of the local density approximation (LDA) for the short-range functional. Moreover, this analysis leads also to new simple approximations for the short-range exchange and correlation energies improving the LDA.Comment: 18 pages, 14 figures, to be published in Phys. Rev.

Statistical Mechanics and the Physics of the Many-Particle Model Systems

The development of methods of quantum statistical mechanics is considered in light of their applications to quantum solid-state theory. We discuss fundamental problems of the physics of magnetic materials and the methods of the quantum theory of magnetism, including the method of two-time temperature Green's functions, which is widely used in various physical problems of many-particle systems with interaction. Quantum cooperative effects and quasiparticle dynamics in the basic microscopic models of quantum theory of magnetism: the Heisenberg model, the Hubbard model, the Anderson Model, and the spin-fermion model are considered in the framework of novel self-consistent-field approximation. We present a comparative analysis of these models; in particular, we compare their applicability for description of complex magnetic materials. The concepts of broken symmetry, quantum protectorate, and quasiaverages are analyzed in the context of quantum theory of magnetism and theory of superconductivity. The notion of broken symmetry is presented within the nonequilibrium statistical operator approach developed by D.N. Zubarev. In the framework of the latter approach we discuss the derivation of kinetic equations for a system in a thermal bath. Finally, the results of investigation of the dynamic behavior of a particle in an environment, taking into account dissipative effects, are presented.Comment: 77 pages, 1 figure, Refs.37

The rigid-band model

The present status of the rigid-band model of an alloy is reviewed with particular reference to the work of Cohen and Heine. A short account is also given of a recent attempt to obtain more quantitative information about the distortion of energy surfaces on alloying, by a direct calculation using the tight-binding approximation with à lattice of square potential wells.On passe en revue l'état actuel des connaissances sur le modèle des bandes rigides d'un alliage, avec une référence particulière du travail de Cohen et Heine. On donne également un court aperçu d'une étude récente, consistant à essayer d'obtenir plus de renseignements quantitatifs sur la distorsion des surfaces d'énergie dans les alliages, par un calcul direct utilisant l'approximation des liaisons fortes et un modèle de puits de potentiels carrés