Rydberg transition frequencies from the Local Density Approximation

A method is given that extracts accurate Rydberg excitations from LDA density functional calculations, despite the short-ranged potential. For the case of He and Ne, the asymptotic quantum defects predicted by LDA are in less than 5% error, yielding transition frequency errors of less than 0.1eV.Comment: 4 pages, 6 figures, submitted to Phys. Rev. Let

Clustering Phase Transitions and Hysteresis: Pitfalls in Constructing Network Ensembles

Ensembles of networks are used as null models in many applications. However, simple null models often show much less clustering than their real-world counterparts. In this paper, we study a model where clustering is enhanced by means of a fugacity term as in the Strauss (or "triangle") model, but where the degree sequence is strictly preserved -- thus maintaining the quenched heterogeneity of nodes found in the original degree sequence. Similar models had been proposed previously in [R. Milo et al., Science 298, 824 (2002)]. We find that our model exhibits phase transitions as the fugacity is changed. For regular graphs (identical degrees for all nodes) with degree k > 2 we find a single first order transition. For all non-regular networks that we studied (including Erdos - Renyi and scale-free networks) we find multiple jumps resembling first order transitions, together with strong hysteresis. The latter transitions are driven by the sudden emergence of "cluster cores": groups of highly interconnected nodes with higher than average degrees. To study these cluster cores visually, we introduce q-clique adjacency plots. We find that these cluster cores constitute distinct communities which emerge spontaneously from the triangle generating process. Finally, we point out that cluster cores produce pitfalls when using the present (and similar) models as null models for strongly clustered networks, due to the very strong hysteresis which effectively leads to broken ergodicity on realistic time scales.Comment: 13 pages, 11 figure

Network dynamics of ongoing social relationships

Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of response times (times between consecutive contacts of different direction between two actors) that has a power-law shape over a large range. We also argue that the distribution of relationship duration (the time between the first and last contacts between actors) is exponentially decaying. Methods to reanalyze the data to compensate for the finite sampling time are proposed. We find that the degree distribution for networks of ongoing contacts fits better to a power-law than the degree distribution of the network of accumulated contacts do. We see that the clustering and assortative mixing coefficients are of the same order for networks of ongoing and accumulated contacts, and that the structural fluctuations of the former are rather large.Comment: to appear in Europhys. Let

Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small-worlds that includes {\it declustered} networks, and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure

Magnetism and local distortions near carbon impurity in γ\gamma-iron

Local perturbations of crystal and magnetic structure of $\gamma$-iron near carbon interstitial impurity is investigated by {\it ab initio} electronic structure calculations. It is shown that the carbon impurity creates locally a region of ferromagnetic ordering with substantial tetragonal distortions. Exchange integrals and solution enthalpy are calculated, the latter being in a very good agreement with experimental data. Effect of the local distortions on the carbon-carbon interactions in $\gamma$-iron is discussed.Comment: 4 pages 3 figures. Final version, accepted to Phys.Rev. Let

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded, subsections reorganized, appendix and new references adde

Comment on "On the importance of the free energy for elasticity under pressure"

Marcus et al. (Marcus P, Ma H and Qiu S L 2002 J. Phys.: Condens. Matter 14 L525) claim that thermodynamic properties of materials under pressure must be computed using the Gibbs free energy $G$, rather than the internal energy $E$. Marcus et al. state that ``The minima of $G$, but not of $E$, give the equilibrium structure; the second derivatives of $G$, but not of $E$, with respect to strains at the equilibrium structure give the equilibrium elastic constants.'' Both statements are incorrect.Comment: Commen

Systematic corrections to the measured cosmological constant as a result of local inhomogeneity

We calculate the systematic inhomogeneity-induced correction to the cosmological constant that one would infer from an analysis of the luminosities and redshifts of Type Ia supernovae, assuming a homogeneous universe. The calculation entails a post-Newtonian expansion within the framework of second order perturbation theory, wherein we consider the effects of subhorizon density perturbations in a flat, dust dominated universe. Within this formalism, we calculate luminosity distances and redshifts along the past light cone of an observer. The resulting luminosity distance-redshift relation is fit to that of a homogeneous model in order to deduce the best-fit cosmological constant density Omega_Lambda. We find that the luminosity distance-redshift relation is indeed modified, by a small fraction of order 10^{-5}. When fitting this perturbed relation to that of a homogeneous universe, we find that the inferred cosmological constant can be surprisingly large, depending on the range of redshifts sampled. For a sample of supernovae extending from z=0.02 out to z=0.15, we find that Omega_Lambda=0.004. The value of Omega_Lambda has a large variance, and its magnitude tends to get larger for smaller redshifts, implying that precision measurements from nearby supernova data will require taking this effect into account. However, we find that this effect is likely too small to explain the observed value of Omega_Lambda=0.7. There have been previous claims of much larger backreaction effects. By contrast to those calculations, our work is directly related to how observers deduce cosmological parameters from astronomical data.Comment: 28 pages, 3 figures, revtex4; v2: corrected comments and the section on previous work; v3: clarified wording. References adde