Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach

We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation. The form of the gluon propagator at low momenta is modeled by a 2-parameter ansatz fitting the weak pion decay constant. The quarks are confined in the sense that the quark propagator does not have a pole at timelike momenta. We determine the ground state mass in the vector channel from the Euclidean time Fourier transform of the correlator, which has an exponential falloff at large times. The ground state mass lies around 590 MeV and is almost independent of the model form for the gluon propagator. This method allows us to stay in Euclidean space and to avoid analytic continuation of the quark or gluon propagators into the timelike region.Comment: 21 pages (REVTEX), 8 Postscript figure

Local Casimir Energy For Solitons

Direct calculation of the one-loop contributions to the energy density of bosonic and supersymmetric phi-to-the-fourth kinks exhibits: (1) Local mode regularization. Requiring the mode density in the kink and the trivial sectors to be equal at each point in space yields the anomalous part of the energy density. (2) Phase space factorization. A striking position-momentum factorization for reflectionless potentials gives the non-anomalous energy density a simple relation to that for the bound state. For the supersymmetric kink, our expression for the energy density (both the anomalous and non-anomalous parts) agrees with the published central charge density, whose anomalous part we also compute directly by point-splitting regularization. Finally we show that, for a scalar field with arbitrary scalar background potential in one space dimension, point-splitting regularization implies local mode regularization of the Casimir energy density.Comment: 18 pages. Numerous new clarifications and additions, of which the most important may be the direct derivation of local mode regularization from point-splitting regularization for the bosonic kink in 1+1 dimension

Gravitational Collapse of Phantom Fluid in (2+1)-Dimensions

This investigation is devoted to the solutions of Einstein's field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial pressure vanishes, we show that there exists a solution of the equations that represents the gravitational collapse of an anisotropic fluid, and this collapse will eventually form a black hole, even when it is constituted by the phantom energy.Comment: 10 page

Critical Collapse of Cylindrically Symmetric Scalar Field in Four-Dimensional Einstein's Theory of Gravity

Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their local and global properties are investigated and found that they represent gravitational collapse of a massless scalar field. In some cases the collapse forms black holes with cylindrical symmetry, while in the other cases it does not. The linear perturbations of these solutions are also studied and given in closed form. From the spectra of the unstable eigen-modes, it is found that there exists one solution that has precisely one unstable mode, which may represent a critical solution, sitting on a boundary that separates two different basins of attraction in the phase space.Comment: Some typos are corrected. The final version to appear in Phys. Rev.

Direct measurement of optical quasidistribution functions: multimode theory and homodyne tests of Bell's inequalities

We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as non-unit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's inequalities by measuring joint two-mode quasidistribution functions under locality conditions by photon counting. We determine the range of parameters of the experimental setup that enable violation of Bell's inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of non-degenerate parametric down-conversion.Comment: 18 pages, 7 figure

Neighbouring plants modify maize root foraging for phosphorus:coupling nutrients and neighbours for improved nutrient-use efficiency

Nutrient distribution and neighbours can impact plant growth, but how neighbours shape root‐foraging strategy for nutrients is unclear. Here, we explore new patterns of plant foraging for nutrients as affected by neighbours to improve nutrient acquisition. Maize (Zea mays) was grown alone (maize), or with maize (maize/maize) or faba bean (Vicia faba) (maize/faba bean) as a neighbour on one side and with or without a phosphorus (P)‐rich zone on the other in a rhizo‐box experiment. Maize demonstrated root avoidance in maize/maize, with reduced root growth in ‘shared’ soil, and increased growth away from its neighbours. Conversely, maize proliferated roots in the proximity of neighbouring faba bean roots that had greater P availability in the rhizosphere (as a result of citrate and acid phosphatase exudation) compared with maize roots. Maize proliferated more roots, but spent less time to reach, and grow out of, the P patches away from neighbours in the maize/maize than in the maize/faba bean experiment. Maize shoot biomass and P uptake were greater in the heterogeneous P treatment with maize/faba bean than with maize/maize system. The foraging strategy of maize roots is an integrated function of heterogeneous distribution of nutrients and neighbouring plants, thus improving nutrient acquisition and maize growth. Understanding the foraging patterns is critical for optimizing nutrient management in crops

Why does fertilization reduce plant species diversity? Testing three competition-based hypotheses

1 Plant species diversity drops when fertilizer is added or productivity increases. To explain this, the total competition hypothesis predicts that competition above ground and below ground both become more important, leading to more competitive exclusion, whereas the light competition hypothesis predicts that a shift from below-ground to above-ground competition has a similar effect. The density hypothesis predicts that more above-ground competition leads to mortality of small individuals of all species, and thus a random loss of species from plots. 2 Fertilizer was added to old field plots to manipulate both below-ground and above-ground resources, while shadecloth was used to manipulate above-ground resources alone in tests of these hypotheses. 3 Fertilizer decreased both ramet density and species diversity, and the effect remained significant when density was added as a covariate. Density effects explained only a small part of the drop in diversity with fertilizer. 4 Shadecloth and fertilizer reduced light by the same amount, but only fertilizer reduced diversity. Light alone did not control diversity, as the light competition hypothesis would have predicted, but the combination of above-ground and below-ground competition caused competitive exclusion, consistent with the total competition hypothesis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75695/1/j.1365-2745.2001.00662.x.pd

Psychosocial Treatment of Children in Foster Care: A Review

A substantial number of children in foster care exhibit psychiatric difficulties. Recent epidemiologi-cal and historical trends in foster care, clinical findings about the adjustment of children in foster care, and adult outcomes are reviewed, followed by a description of current approaches to treatment and extant empirical support. Available interventions for these children can be categorized as either symptom-focused or systemic, with empirical support for specific methods ranging from scant to substantial. Even with treatment, behavioral and emotional problems often persist into adulthood, resulting in poor functional outcomes. We suggest that self-regulation may be an important mediat-ing factor in the appearance of emotional and behavioral disturbance in these children