Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other thing, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the G0W0 approximation. This exchange-correlation kernel as well as its complement analogue associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long-range and short-range interaction effects.Comment: 14 pages, 14 figures, to be published in Phys. Rev.

Disorder-Induced Resistive Anomaly Near Ferromagnetic Phase Transitions

We show that the resistivity rho(T) of disordered ferromagnets near, and above, the Curie temperature T_c generically exhibits a stronger anomaly than the scaling-based Fisher-Langer prediction. Treating transport beyond the Boltzmann description, we find that within mean-field theory, d\rho/dT exhibits a |T-T_c|^{-1/2} singularity near T_c. Our results, being solely due to impurities, are relevant to ferromagnets with low T_c, such as SrRuO3 or diluted magnetic semiconductors, whose mobility near T_c is limited by disorder.Comment: 5 pages, 3 figures; V2: with a few clarifications, as publishe

Metal–insulator transition in 2D as a quantum phase transition

We discuss the metal–insulator transition phenomenon in two dimensions in terms of a quantum critical point that controls a range of the low temperature insulator region as well as the usual quantum critical sector. We show that this extended range of criticality permits a determination of both the dynamical critical exponent z and the correlation length critical exponent ν from published data from a single experiment in the insulator critical region. The resulting value of the product zν is consistent with the temperature dependence of the resistance in the quantum critical sector. This provides strong quantitative evidence for the presence of a quantum critical point

Statistical characterization of the forces on spheres in an upflow of air

The dynamics of a sphere fluidized in a nearly-levitating upflow of air were previously found to be identical to those of a Brownian particle in a two-dimensional harmonic trap, consistent with a Langevin equation [Ojha {\it et al.}, Nature {\bf 427}, 521 (2004)]. The random forcing, the drag, and the trapping potential represent different aspects of the interaction of the sphere with the air flow. In this paper we vary the experimental conditions for a single sphere, and report on how the force terms in the Langevin equation scale with air flow speed, sphere radius, sphere density, and system size. We also report on the effective interaction potential between two spheres in an upflow of air.Comment: 7 pages, experimen

Conserving Approximations in Time-Dependent Density Functional Theory

In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid nineties. Due to this feature the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nano-scale systems.Comment: 11 pages, 4 figures, revised versio

The on-top pair-correlation density in the homogeneous electron liquid

The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.Comment: 8 pages, 4 figure