Reduced Density-Matrix Functional Theory: correlation and spectroscopy

In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard molecule at 1/4 and 1/2 filling as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison we also report the results of the $GW$ approximation, where the self-energy functional is approximated, but no further hypothesis are made concerning the approximations of the observables. In particular we focus on the atomic limit, where the two sites of the molecule are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard molecule at 1/2 filling with or without a spin-symmetry-broken ground state, allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in $GW$ the signature of strong correlation are present in the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover we show how the spectroscopic properties change from one spin structure to the other. Our findings can be generalized to other situations, which allows us to make connections to real materials and experiment

The role of relativity in the optical response of gold within the time-dependent current-density-functional theory

We included relativistic effects in the formulation of the time-dependent current-density-functional theory for the calculation of linear response properties of metals [P. Romaniello and P. L. de Boeij, Phys. Rev. B (to be published)]. We treat the dominant scalar-relativistic effects using the zeroth-order regular approximation in the ground-state density-functional theory calculations, as well as in the time-dependent response calculations. The results for the dielectric function of gold calculated in the spectral range of 0-10 eV are compared with experimental data reported in literature and recent ellipsometric measurements. As well known, relativistic effects strongly influence the color of gold. We find that the onset of interband transitions is shifted from around 3.5 eV, obtained in a nonrelativistic calculation, to around 1.9 eV when relativity is included. With the inclusion of the scalar-relativistic effects there is an overall improvement of both real and imaginary parts of the dielectric function over the nonrelativistic ones. Nevertheless some important features in the absorption spectrum are not well reproduced, but can be explained in terms of spin-orbit coupling effects. The remaining deviations are attributed to the underestimation of the interband gap (5d-6sp band gap) in the local-density approximation and to the use of the adiabatic local-density approximation in the response calculation. (c) 2005 American Institute of Physics

Classical Cepheids, what else?

We present new and independent estimates of the distances to the Magellanic Clouds (MCs) using near-infrared (NIR) and optical--NIR period--Wesenheit (PW) relations. The slopes of the PW relations are, within the dispersion, linear over the entire period range and independent of metal content. The absolute zero points were fixed using Galactic Cepheids with distances based on the infrared surface-brightness method. The true distance modulus we found for the Large Magellanic Cloud---$(m-M)_0 = 18.48 \pm 0.01 \pm 0.10$ mag---and the Small Magellanic Cloud---$(m-M)_0 = 18.94 \pm 0.01 \pm 0.10$ mag---agree quite well with similar distance determinations based on robust distance indicators. We also briefly discuss the evolutionary and pulsation properties of MC Cepheids

WFPC2 Observations of NGC 454: an Interacting Pair of Galaxies

We present WFPC2 images in the F450W, F606W and F814W filters of the interacting pair of galaxies NGC 454. Our data indicate that the system is in the early stages of interaction. A population of young star-clusters has formed around the late component, and substantial amounts of gas have sunk into the center of the earlier component, where it has not yet produced significant visible star formation or nuclear activity. We have photometric evidence that the star-clusters have strong line emission, which indicate the presence of a substantial component of hot, massive stars which formed less than 5-10 Myrs ago.Comment: 14 pages, 4 figures, Latex (AAS macros), ApJL in pres

Approximations for many-body Green's functions: insights from the fundamental equations

Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. In the present work we apply a linear response expansion in order to obtain insights in various approximations for Green's functions calculations. The expansion leads to an effective screening, while keeping the effects of the interaction to all orders. In order to study various aspects of the resulting equations we discretize them, and retain only one point in space, spin, and time for all variables. Within this one-point model we obtain an explicit solution for the Green's function, which allows us to explore the structure of the general family of solutions, and to determine the specific solution that corresponds to the physical one. Moreover we analyze the performances of established approaches like $GW$ over the whole range of interaction strength, and we explore alternative approximations. Finally we link certain approximations for the exact solution to the corresponding manipulations for the differential equation which produce them. This link is crucial in view of a generalization of our findings to the real (multidimensional functional) case where only the differential equation is known.Comment: 17 pages, 7 figure

The Distance to NGC 5128 (Centaurus A)

In this paper we review the various high precision methods that are now available to determine the distance to NGC 5128. These methods include: Cepheids, TRGB (tip of the red giant branch), PNLF (planetary nebula luminosity function), SBF (surface brightness fluctuations) and Long Period Variable (LPV) Mira stars. From an evaluation of these methods and their uncertainties, we derive a best-estimate distance of 3.8 +- 0.1 Mpc to NGC 5128 and find that this mean is now well supported by the current data. We also discuss the role of NGC 5128 more generally for the extragalactic distance scale as a testbed for the most direct possible comparison among these key methods.Comment: in press PASA; minor text change

On the distance of the Magellanic Clouds using Cepheid NIR and optical-NIR Period Wesenheit Relations

We present the largest near-infrared (NIR) data sets, $JHKs$, ever collected for classical Cepheids in the Magellanic Clouds (MCs). We selected fundamental (FU) and first overtone (FO) pulsators, and found 4150 (2571 FU, 1579 FO) Cepheids for Small Magellanic Cloud (SMC) and 3042 (1840 FU, 1202 FO) for Large Magellanic Cloud (LMC). Current sample is 2--3 times larger than any sample used in previous investigations with NIR photometry. We also discuss optical $VI$ photometry from OGLE-III. NIR and optical--NIR Period-Wesenheit (PW) relations are linear over the entire period range ($0.0<\log P_{\rm FU} \le1.65$) and their slopes are, within the intrinsic dispersions, common between the MCs. These are consistent with recent results from pulsation models and observations suggesting that the PW relations are minimally affected by the metal content. The new FU and FO PW relations were calibrated using a sample of Galactic Cepheids with distances based on trigonometric parallaxes and Cepheid pulsation models. By using FU Cepheids we found a true distance moduli of $18.45\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (LMC) and $18.93\pm0.02{\rm(random)}\pm0.10{\rm(systematic)}$ mag (SMC). These estimates are the weighted mean over ten PW relations and the systematic errors account for uncertainties in the zero-point and in the reddening law. We found similar distances using FO Cepheids ($18.60\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [LMC] and $19.12\pm0.03{\rm(random)}\pm0.10{\rm(systematic)}$ mag [SMC]). These new MC distances lead to the relative distance, $\Delta\mu=0.48\pm0.03$ mag (FU, $\log P=1$) and $\Delta\mu=0.52\pm0.03$ mag (FO, $\log P=0.5$),which agrees quite well with previous estimates based on robust distance indicators.Comment: 17 pages, 7 figure

Performance of the Vignale-Kohn functional in the linear response of metals

Recently the linear response of metallic solids has been formulated within the time-dependent current-density-functional approach [Romaniello and de Boeij, Phys. Rev. B 71, 155108 (2005)]. The implementation, which originally used only the adiabatic local density approximation for the exchange-correlation kernel is extended in order to include also the Vignale-Kohn current functional. Within this approximation the exchange-correlation kernel is frequency dependent, thus relaxation effects due to electron-electron scattering can now be taken into account and some deficiencies of the adiabatic local density approximation (ALDA), as the absence of the low-frequency Drude-like tail in absorption spectra, can be cured. We strictly follow the previous formulation of the linear response of semiconductors by using the Vignale-Kohn functional [Berger, de Boeij, and van Leeuwen, Phys. Rev. B 71, 155104 (2005)]. The self-consistent equations for the interband and intraband contributions to the induced density and current density, which are completely decoupled within the ALDA and in the long-wavelength limit, now remain coupled. We present our results calculated for the optical properties of the noble metals Cu, Ag, and Au and we compare them with measurements found in literature. In the case of Au we treat the dominant scalar relativistic effects using the zeroth-order regular approximation in the ground-state density-functional-theory calculations, as well as in the time-dependent response calculations