Pair Excitations and Vertex Corrections in Fermi Fluids

Based on an equations--of--motion approach for time--dependent pair correlations in strongly interacting Fermi liquids, we have developed a theory for describing the excitation spectrum of these systems. Compared to the known ``correlated'' random--phase approximation (CRPA), our approach has the following properties: i) The CRPA is reproduced when pair fluctuations are neglected. ii) The first two energy--weighted sumrules are fulfilled implying a correct static structure. iii) No ad--hoc assumptions for the effective mass are needed to reproduce the experimental dispersion of the roton in 3He. iv) The density response function displays a novel form, arising from vertex corrections in the proper polarisation. Our theory is presented here with special emphasis on this latter point. We have also extended the approach to the single particle self-energy and included pair fluctuations in the same way. The theory provides a diagrammatic superset of the familiar GW approximation. It aims at a consistent calculation of single particle excitations with an accuracy that has previously only been achieved for impurities in Bose liquids.Comment: to be published in: JLTP (2007) Proc. Int. Symp. QFS2006, 1-6 Aug. 2006, Kyoto, Japa

Distance and the pattern of intra-European trade

Given an undirected graph G = (V, E) and subset of terminals T ⊆ V, the element-connectivity κ ′ G (u, v) of two terminals u, v ∈ T is the maximum number of u-v paths that are pairwise disjoint in both edges and non-terminals V \ T (the paths need not be disjoint in terminals). Element-connectivity is more general than edge-connectivity and less general than vertex-connectivity. Hind and Oellermann [21] gave a graph reduction step that preserves the global element-connectivity of the graph. We show that this step also preserves local connectivity, that is, all the pairwise element-connectivities of the terminals. We give two applications of this reduction step to connectivity and network design problems. • Given a graph G and disjoint terminal sets T1, T2,..., Tm, we seek a maximum number of elementdisjoint Steiner forests where each forest connects each Ti. We prove that if each Ti is k element k connected then there exist Ω( log hlog m) element-disjoint Steiner forests, where h = | i Ti|. If G is planar (or more generally, has fixed genus), we show that there exist Ω(k) Steiner forests. Our proofs are constructive, giving poly-time algorithms to find these forests; these are the first non-trivial algorithms for packing element-disjoint Steiner Forests. • We give a very short and intuitive proof of a spider-decomposition theorem of Chuzhoy and Khanna [12] in the context of the single-sink k-vertex-connectivity problem; this yields a simple and alternative analysis of an O(k log n) approximation. Our results highlight the effectiveness of the element-connectivity reduction step; we believe it will find more applications in the future

Light scattering from disordered overlayers of metallic nanoparticles

We develop a theory for light scattering from a disordered layer of metal nanoparticles resting on a sample. Averaging over different disorder realizations is done by a coherent potential approximation. The calculational scheme takes into account effects of retardation, multipole excitations, and interactions with the sample. We apply the theory to a system similar to the one studied experimentally by Stuart and Hall [Phys. Rev. Lett. {\bf 80}, 5663 (1998)] who used a layered Si/SiO$_2$/Si sample. The calculated results agree rather well with the experimental ones. In particular we find conspicuous maxima in the scattering intensity at long wavelengths (much longer than those corresponding to plasmon resonances in the particles). We show that these maxima have their origin in interference phenomena in the layered sample.Comment: 19 pages, 12 figure

Residual meson-meson interaction from lattice gauge simulation in a simple QED model

The residual interaction for a meson-meson system is computed utilizing the cumulant, or cluster, expansion of the momentum-space time correlation matrix. The cumulant expansion serves to define asymptotic, or free, meson-meson operators. The definition of an effective interaction is then based on a comparison of the full (interacting) and the free (noninteracting) time correlation matrices. The proposed method, which may straightforwardly be transcribed to other hadron-hadron systems, here is applied to a simple 2+1 dimensional U(1) lattice gauge model tuned such that it is confining. Fermions are treated in the staggered scheme. The effective interaction exhibits a repulsive core and attraction at intermediate relative distances. These findings are consistent with an earlier study of the same model utilizing L\"{u}scher's method where scattering phase shifts are obtained directly.Comment: 28 pages, compressed postscript fil

The Van der Waals interaction of the hydrogen molecule - an exact local energy density functional

We verify that the van der Waals interaction and hence all dispersion interactions for the hydrogen molecule given by: W"= -{A/R^6}-{B/R^8}-{C/R^10}- ..., in which R is the internuclear separation, are exactly soluble. The constants A=6.4990267..., B=124.3990835 ... and C=1135.2140398... (in Hartree units) first obtained approximately by Pauling and Beach (PB) [1] using a linear variational method, can be shown to be obtainable to any desired accuracy via our exact solution. In addition we shall show that a local energy density functional can be obtained, whose variational solution rederives the exact solution for this problem. This demonstrates explicitly that a static local density functional theory exists for this system. We conclude with remarks about generalising the method to other hydrogenic systems and also to helium.Comment: 11 pages, 13 figures and 28 reference

Determination of the Deep Inelastic Contribution to the Generalised Gerasimov-Drell-Hearn Integral for the Proton and Neutron

The virtual photon absorption cross section differences [sigma_1/2-sigma_3/2] for the proton and neutron have been determined from measurements of polarised cross section asymmetries in deep inelastic scattering of 27.5 GeV longitudinally polarised positrons from polarised 1H and 3He internal gas targets. The data were collected in the region above the nucleon resonances in the kinematic range nu < 23.5 GeV and 0.8 GeV**2 < Q**2 < 12 GeV**2. For the proton the contribution to the generalised Gerasimov-Drell-Hearn integral was found to be substantial and must be included for an accurate determination of the full integral. Furthermore the data are consistent with a QCD next-to-leading order fit based on previous deep inelastic scattering data. Therefore higher twist effects do not appear significant.Comment: 6 pages, 3 figures, 1 table, revte

Observation of a Coherence Length Effect in Exclusive Rho^0 Electroproduction

Exclusive incoherent electroproduction of the rho^0(770) meson from 1H, 2H, 3He, and 14N targets has been studied by the HERMES experiment at squared four-momentum transfer Q**2>0.4 GeV**2 and positron energy loss nu from 9 to 20 GeV. The ratio of the 14N to 1H cross sections per nucleon, known as the nuclear transparency, was found to decrease with increasing coherence length of quark-antiquark fluctuations of the virtual photon. The data provide clear evidence of the interaction of the quark- antiquark fluctuations with the nuclear medium.Comment: RevTeX, 5 pages, 3 figure

Measurement of the Charged Multiplicities in b, c and Light Quark Events from Z0 Decays

Average charged multiplicities have been measured separately in $b$, $c$ and light quark ($u,d,s$) events from $Z^0$ decays measured in the SLD experiment. Impact parameters of charged tracks were used to select enriched samples of $b$ and light quark events, and reconstructed charmed mesons were used to select $c$ quark events. We measured the charged multiplicities: $\bar{n}_{uds} = 20.21 \pm 0.10 (\rm{stat.})\pm 0.22(\rm{syst.})$, $\bar{n}_{c} = 21.28 \pm 0.46(\rm{stat.}) ^{+0.41}_{-0.36}(\rm{syst.})$ $\bar{n}_{b} = 23.14 \pm 0.10(\rm{stat.}) ^{+0.38}_{-0.37}(\rm{syst.})$, from which we derived the differences between the total average charged multiplicities of $c$ or $b$ quark events and light quark events: $\Delta \bar{n}_c = 1.07 \pm 0.47(\rm{stat.})^{+0.36}_{-0.30}(\rm{syst.})$ and $\Delta \bar{n}_b = 2.93 \pm 0.14(\rm{stat.})^{+0.30}_{-0.29}(\rm{syst.})$. We compared these measurements with those at lower center-of-mass energies and with perturbative QCD predictions. These combined results are in agreement with the QCD expectations and disfavor the hypothesis of flavor-independent fragmentation.Comment: 19 pages LaTex, 4 EPS figures, to appear in Physics Letters

Flavor Decomposition of the Polarized Quark Distributions in the Nucleon from Inclusive and Semi-inclusive Deep-inelastic Scattering

Spin asymmetries of semi-inclusive cross sections for the production of positively and negatively charged hadrons have been measured in deep-inelastic scattering of polarized positrons on polarized hydrogen and 3He targets, in the kinematic range 0.023<x<0.6 and 1 GeV^2<Q^2<10 GeV^2. Polarized quark distributions are extracted as a function of x for up $(u+u_bar) and down (d+d_bar) flavors. The up quark polarization is positive and the down quark polarization is negative in the measured range. The polarization of the sea is compatible with zero. The first moments of the polarized quark distributions are presented. The isospin non-singlet combination Delta_q_3 is consistent with the prediction based on the Bjorken sum rule. The moments of the polarized quark distributions are compared to predictions based on SU(3)_f flavor symmetry and to a prediction from lattice QCD.Comment: 14 pages, 6 figures (eps format), 10 tables in Latex New version contains tables of asymmetries and correlation matri

Velocity-space sensitivity of the time-of-flight neutron spectrometer at JET

The velocity-space sensitivities of fast-ion diagnostics are often described by so-called weight functions. Recently, we formulated weight functions showing the velocity-space sensitivity of the often dominant beam-target part of neutron energy spectra. These weight functions for neutron emission spectrometry (NES) are independent of the particular NES diagnostic. Here we apply these NES weight functions to the time-of-flight spectrometer TOFOR at JET. By taking the instrumental response function of TOFOR into account, we calculate time-of-flight NES weight functions that enable us to directly determine the velocity-space sensitivity of a given part of a measured time-of-flight spectrum from TOFOR