Discontinuity of the chemical potential in reduced-density-matrix-functional theory

We present a novel method for calculating the fundamental gap. To this end, reduced-density-matrix-functional theory is generalized to fractional particle number. For each fixed particle number, $M$, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to a function, $E_{\mathrm{tot}}^M$, whose derivative with respect to the particle number has a discontinuity identical to the gap. In contrast to density functional theory, the energy minimum is generally not a stationary point of the total-energy functional. Numerical results, presented for alkali atoms, the LiH molecule, the periodic one-dimensional LiH chain, and solid Ne, are in excellent agreement with CI calculations and/or experimental data.Comment: 9 pages, 3 figures, version as publishe

Attention does not affect multisensory cue weighting

Humans gather information about their environment from multiple sensory channels. It seems that cues from separate sensory modalities (e.g., vision and haptics) are combined in a statistically optimal way according to a maximum-likelihood estimator (Ernst Banks, 2002). Ernst and Banks showed that for bi-modal perceptual estimates, the weight attributed to one sensory channel changes when its relative reliability is modified by increasing the noise associated to its signal. Here we address the question as to whether selectively increasing the attentional load of one sensory channel does affect the weighting of cues from different sensory channels. In our experiment, subjects’ main-task was to estimate the size of a raised bar using vision alone, haptics alone, or both modalities combined. Their performance in the main-task condition alone is compared to the performance obtained when a concurrent visual ‘distractor’-task is performed. We found that vision-based estimates are more affected by a visual ‘distractor’ than the haptics-based estimates. Thus, attention is indeed selectively detracted from the visual modality. Moreover, we found that the cue weighting is not affected by adding the visual ‘distractor’-task. Therefore we can conclude that multisensory integration occurs at an early stage of processing and is not affected by attention

Open shells in reduced-density-matrix-functional theory

Reduced-density-matrix-functional theory is applied to open-shell systems. We introduce a spin-restricted formulation by appropriately expressing approximate correlation-energy functionals in terms of spin-dependent occupation numbers and spin-independent natural orbitals. We demonstrate that the additional constraint of total-spin conservation is indispensable for the proper treatment of open-shell systems. The formalism is applied to the first-row open-shell atoms. The obtained ground-state energies are in very good agreement with the exact values as well as other state of the art quantum chemistry calculationsComment: 4 pages, 2 figures, corrected typo

Exchange-energy functionals for finite two-dimensional systems

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.Comment: 5 pages, 3 figure

Elastic moduli approximation of higher symmetry for the acoustical properties of an anisotropic material

The issue of how to define and determine an optimal acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are defined as those which minimize the mean squared difference in the acoustical tensors between the given moduli and all possible moduli of a chosen higher material symmetry. The solution is shown to be identical to minimizing a Euclidean distance function, or equivalently, projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.Comment: 20 page

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

Current cosmological constraints from a 10 parameter CMB analysis

We compute the constraints on a ``standard'' 10 parameter cold dark matter (CDM) model from the most recent CMB and data and other observations, exploring 30 million discrete models and two continuous parameters. Our parameters are the densities of CDM, baryons, neutrinos, vacuum energy and curvature, the reionization optical depth, and the normalization and tilt for both scalar and tensor fluctuations. Our strongest constraints are on spatial curvature, -0.24 < Omega_k < 0.38, and CDM density, h^2 Omega_cdm <0.3, both at 95%. Including SN 1a constraints gives a positive cosmological constant at high significance. We explore the robustness of our results to various assumptions. We find that three different data subsets give qualitatively consistent constraints. Some of the technical issues that have the largest impact are the inclusion of calibration errors, closed models, gravity waves, reionization, nucleosynthesis constraints and 10-dimensional likelihood interpolation.Comment: Replaced to match published ApJ version. More details added. 13 ApJ pages. CMB movies and color figs at http://www.hep.upenn.edu/~max/10par_frames.html or from [email protected]

Dark Energy and the Statistical Study of the Observed Image Separations of the Multiply Imaged Systems in the CLASS Statistical Sample

The present day observations favour a universe which is flat, accelerated and composed of $\sim 1/3$ matter (baryonic + dark) and $\sim 2/3$ of a negative pressure component, usually referred to as dark energy or quintessence. The Cosmic Lens All Sky Survey (CLASS), the largest radio-selected galactic mass scale gravitational lens search project to date, has resulted in the largest sample suitable for statistical analyses. In the work presented here, we exploit observed image separations of the multiply imaged lensed radio sources in the sample. We use two different tests: (1) image separation distribution function $n(\Delta\theta)$ of the lensed radio sources and (2) {\dtheta}_{\mathrm{pred}} vs {\dtheta}_{\mathrm{obs}} as observational tools to constrain the cosmological parameters $w$ and \Om. The results are in concordance with the bounds imposed by other cosmological tests.Comment: 20 pages latex; Modified " Results and Discussion " section, new references adde