Exact Kohn-Sham potential of strongly correlated finite systems

The dissociation of molecules, even the most simple hydrogen molecule, cannot be described accurately within density functional theory because none of the currently available functionals accounts for strong on-site correlation. This problem has led to a discussion of properties that the local Kohn-Sham potential has to satisfy in order to correctly describe strongly correlated systems. We derive an analytic expression for this potential at the dissociation limit and show that the numerical calculations for a one-dimensional two electron model system indeed approach and reach this limit. It is shown that the functional form of the potential is universal, i.e. independent of the details of the system.Comment: 17 pages, 3 figures, submitted to JC

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a novel scheme to bring reduced density matrix functional theory (RDMFT) into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules

The Cosmic Lens All-Sky Survey parent population - I. Sample selection and number counts

We present the selection of the Jodrell Bank Flat-spectrum (JBF) radio source sample, which is designed to reduce the uncertainties in the Cosmic Lens All-Sky Survey (CLASS) gravitational lensing statistics arising from the lack of knowledge about the parent population luminosity function. From observations at 4.86 GHz with the Very Large Array, we have selected a sample of 117 flat-spectrum radio sources with flux densities greater than 5 mJy. These sources were selected in a similar manner to the CLASS complete sample and are therefore representative of the parent population at low flux densities. The vast majority (~90 per cent) of the JBF sample are found to be compact on the arcsecond scales probed here and show little evidence of any extended radio jet emission. Using the JBF and CLASS complete samples we find the differential number counts slope of the parent population above and below the CLASS 30 mJy flux density limit to be -2.07+/-0.02 and -1.96+/-0.12, respectively.Comment: 10 pages, 4 figures, accepted for publication in MNRA

Gravitational lensing statistics with extragalactic surveys. II. Analysis of the Jodrell Bank-VLA Astrometric Survey

We present constraints on the cosmological constant $\lambda_{0}$ from gravitational lensing statistics of the Jodrell Bank-VLA Astrometric Survey (JVAS). Although this is the largest gravitational lens survey which has been analysed, cosmological constraints are only comparable to those from optical surveys. This is due to the fact that the median source redshifts of JVAS are lower, which leads to both relatively fewer lenses in the survey and a weaker dependence on the cosmological parameters. Although more approximations have to be made than is the case for optical surveys, the consistency of the results with those from optical gravitational lens surveys and other cosmological tests indicate that this is not a major source of uncertainty in the results. However, joint constraints from a combination of radio and optical data are much tighter. Thus, a similar analysis of the much larger Cosmic Lens All-Sky Survey should provide even tighter constraints on the cosmological constant, especially when combined with data from optical lens surveys. At 95% confidence, our lower and upper limits on $\lambda_{0}-\Omega_{0}$, using the JVAS lensing statistics information alone, are respectively -2.69 and 0.68. For a flat universe, these correspond to lower and upper limits on \lambda_{0} of respectively -0.85 and 0.84. Using the combination of JVAS lensing statistics and lensing statistics from the literature as discussed in Quast & Helbig (Paper I) the corresponding $\lambda_{0}-\Omega_{0}$ values are -1.78 and 0.27. For a flat universe, these correspond to lower and upper limits on $\lambda_{0}$ of respectively -0.39 and 0.64.Comment: LaTeX, 9 pages, 18 PostScript files in 6 figures. Paper version available on request. Data available from http://gladia.astro.rug.nl:8000/ceres/data_from_papers/papers.htm

Male-biased gene flow across an avian hybrid zone: evidence from mitochondrial and microsatellite DNA

Mating pattern and gene flow were studied in the contact zone between two morphologically very similar Chiffchaff taxa (Phylloscopus collybita, P. brehmii) in SW France and northern Spain. Mating was assortative in brehmii, but not in collybita. Mixed matings were strongly asymmetric (excess of callybita male x brehmii female pairs), but did produce viable offspring in some cases. Sequence divergence of the mitochondrial cytochrome b gene was 4.6%; Haplotypes segregated significantly with phenotype (only five 'mismatches' among 94 individuals), demonstrating that mitochondrial gene flow was very restricted. The estimated proportion of F-1 hybrids in the reproductive population was significantly lower than expected under a closed population model, indicating strong selection against hybrids. Genetic typing of 101 individuals at four microsatellite loci also showed significant population differentiation, but nuclear gene flow was estimated to be 75 times higher than mitochondrial gene flow. This strong discrepancy is probably due to unisexual hybrid sterility (Haldane's rule). Thus, there is a strong, but incomplete, reproductive barrier between these taxa

Performance of the exact adiabatic density functional to describe Rabi physics

Trabajo presentado al American Physical Society Meeting, celebrado en Boston (US) del 27 de Febrero al 2 de Marzo de 2012.-- Título de la presentación: "Rabi oscillations within TDDFT: the example of the 2 site Hubbard model".Through the exact solution of few-electron systems interacting with a monochromatic laser we study the performance of adiabatic density functionals within time-dependent density-functional theory (TDDFT) to reproduce Rabi oscillations. The non-linear dynamics of the Kohn-Sham (KS) system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We illustrate this effect by comparing the exact time-dependent many-body solution of a He-atom in one dimension and a few-site Hubbard model with the solution of TDDFT-KS equations for different adiabatic exchange-correlation functionals. Preventing the detuning introduces a new strong condition to be satisfied by approximate new xc-functionals.Peer reviewe

Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations

We propose a scheme to bring reduced-density-matrix-functional theory into the realm of density functional theory (DFT) that preserves the accurate density functional description at equilibrium, while incorporating accurately static and left-right correlation effects in molecules and keeping the good computational performance of DFT-based schemes. The key ingredient is to relax the requirement that the local potential is the functional derivative of the energy with respect to the density. Instead, we propose to restrict the search for the approximate natural orbitals within a domain where these orbitals are eigenfunctions of a single-particle Hamiltonian with a local effective potential. In this way, fractional natural occupation numbers are accommodated into Kohn-Sham equations allowing for the description of molecular dissociation without breaking spin symmetry. Additionally, our scheme provides a natural way to connect an energy eigenvalue spectrum to the approximate natural orbitals and this spectrum is found to represent accurately the ionization potentials of atoms and small molecules.N.N.L. acknowledges financial support from the GSRT, Greece, Polynano-Kripis project (Grant No. 447963); N.H. from an Emmy-Noether grant from Deutsche Forschungsgemeinschaft; and A.R. from the European Community’s FP7 through the CRONOS project, grant agreement no. 280879, the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), and Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant: IT578-13).Peer Reviewe

Lensing galaxies: light or dark?

In a recent paper, Hawkins (1997) argues on the basis of statistical studies of double-image gravitational lenses and lens candidates that a large population of dark lenses exists and that these outnumber galaxies with more normal mass-to-light ratios by a factor of 3:1. If correct, this is a very important result for many areas of astronomy including galaxy formation and cosmology. In this paper we discuss our new radio-selected gravitational lens sample, JVAS/CLASS, in order to test and constrain this proposition. We have obtained ground-based and HST images of all multiple-image lens systems in our sample and in 12 cases out of 12 we find the lensing galaxies in the optical and/or near infrared. Our success in finding lensing galaxies creates problems for the dark lens hypothesis. If it is to survive, ad hoc modifications seem to be necessary: only very massive galaxies (more than about one trillion solar masses) can be dark, and the cutoff in mass must be sharp. Our finding of lens galaxies in all the JVAS/CLASS systems is complementary evidence which supports the conclusion of Kochanek et al. (1997) that many of the wide-separation optically-selected pairs are physically distinct quasars rather than gravitational lens systems.Comment: 4 pages, 2 included figures, accepted for publication in Astronomy and Astrophysics. Paper version available on request. This replacement amends the text to allow more discussion of the overlap with astro-ph/971016

Quasi-particle energy spectra in local reduced density matrix functional theory

Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C20 isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solidsN.N.L. acknowledges financial support from the GSRT action KPHΠIΣ, project “New multifunctional Nanostructured Materials and Devices – POLYNANO” No. 447963, N.H. from a DFG Emmy-Noether grant, and A.R. from the European Research Council Advanced Grant No. ERC-2010-AdG-267374, Spanish Grant No. FIS2010-21282-C02-01, Grupo Consolidado UPV/EHU (IT578-13), and European Commission Project No. CRONOS(280879-2).Peer Reviewe

Orbitals from local RDMFT: Are they Kohn-Sham or Natural Orbitals?

Recently, an approximate theoretical framework was introduced, called local reduced density matrix functional theory (local-RDMFT), where functionals of the one-body reduced density matrix (1-RDM) are minimized under the additional condition that the optimal orbitals satisfy a single electron Schrödinger equation with a local potential. In the present work, we focus on the character of these optimal orbitals. In particular, we compare orbitals obtained by local-RDMFT with those obtained with the full minimization (without the extra condition) by contrasting them against the exact NOs and orbitals from a density functional calculation using the local density approximation (LDA). We find that the orbitals from local-RMDFT are very close to LDA orbitals, contrary to those of the full minimization that resemble the exact NOs. Since local RDMFT preserves the good quality of the description of strong static correlation, this finding opens the way to a mixed density/density matrix scheme, where Kohn-Sham orbitals obtain fractional occupations from a minimization of the occupation numbers using 1-RDM functionals. This will allow for a description of strong correlation at a cost only minimally higher than a density functional calculation