The Universlity Class of Monopole Condensation in Non-Compact, Quenched Lattice QED

Finite size scaling studies of monopole condensation in noncompact quenched lattice $QED$ indicate an authentic second order phase transition lying in the universality class of four dimensional percolation. Since the upper critical dimension of percolation is six, the measured critical indices are far from mean-field values. We propose a simple set of ratios as the exact critical indices for this transition. The implication of these results for critical points in Abelian gauge theories are discussed.Comment: ILL-(TH)-92-6, CERN-TH.6515/92, 10 pages, no figures available as PS fil

Understanding the assembly of Kepler's compact planetary systems

The Kepler mission has recently discovered a number of exoplanetary systems, such as Kepler-11 and Kepler-32, in which ensembles of several planets are found in very closely packed orbits (often within a few percent of an AU of one another). These compact configurations present a challenge for traditional planet formation and migration scenarios. We present a dynamical study of the assembly of these systems, using an N-body method which incorporates a parametrized model of planet migration in a turbulent protoplanetary disc. We explore a wide parameter space, and find that under suitable conditions it is possible to form compact, close-packed planetary systems via traditional disc-driven migration. We find that simultaneous migration of multiple planets is a viable mechanism for the assembly of tightly-packed planetary systems, as long as the disc provides significant eccentricity damping and the level of turbulence in the disc is modest. We discuss the implications of our preferred parameters for the protoplanetary discs in which these systems formed, and comment on the occurrence and significance of mean-motion resonances in our simulations.Comment: 12 pages, 4 figures, 2 tables. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

On the Interplay of Monopoles and Chiral Symmetry Breaking in Non-Compact Lattice QED

Non-compact lattice QED is simulated for various numbers of fermion species $N_f$ ranging from 8 through 40 by the exact Hybrid Monte Carlo algorithm. Over this range of $N_f$, chiral symmetry breaking is found to be strongly correlated with the effective monopoles in the theory. For $N_f$ between 8 and 16 the chiral symmetry breaking and monopole percolation transitions are second order and coincident. Assuming powerlaw critical behavior, the correlation length exponent for the chiral transition is identical to that of monopole percolation. This result supports the conjecture that monopole percolation ``drives" the nontrivial chiral transition. For $N_f$ between 20 and 32, the monopoles experience a first order condensation transition coincident with a first order chiral transition. For $N_f$ as large as 40 both transitions are strongly suppressed. The data at large N_f (N_f \mathrel {\mathpalette \vereq >} 20) is interpreted in terms of a strongly interacting monopole gas-liquid transition.Comment: Revtex file, 23 pages, hardcopy figures only

Numerical Portrait of a Relativistic BCS Gapped Superfluid

We present results of numerical simulations of the 3+1 dimensional Nambu - Jona-Lasinio (NJL) model with a non-zero baryon density enforced via the introduction of a chemical potential mu not equal to 0. The triviality of the model with a number of dimensions d>=4 is dealt with by fitting low energy constants, calculated analytically in the large number of colors (Hartree) limit, to phenomenological values. Non-perturbative measurements of local order parameters for superfluidity and their related susceptibilities show that, in contrast to the 2+1 dimensional model, the ground-state at high chemical potential and low temperature is that of a traditional BCS superfluid. This conclusion is supported by the direct observation of a gap in the dispersion relation for 0.5<=(mu a)<=0.85, which at (mu a)=0.8 is found to be roughly 15% the size of the vacuum fermion mass. We also present results of an initial investigation of the stability of the BCS phase against thermal fluctuations. Finally, we discuss the effect of splitting the Fermi surfaces of the pairing partners by the introduction of a non-zero isospin chemical potential.Comment: 41 pages, 19 figures, uses axodraw.sty, v2: minor typographical correction

Mesonic Wavefunctions in the three-dimensional Gross-Neveu model

We present results from a numerical study of bound state wavefunctions in the (2+1)-dimensional Gross-Neveu model with staggered lattice fermions at both zero and nonzero temperature. Mesonic channels with varying quantum numbers are identified and analysed. In the strongly coupled chirally broken phase at T=0 the wavefunctions expose effects due to varying the interaction strength more effectively than straightforward spectroscopy. In the weakly coupled chirally restored phase information on fermion - antifermion scattering is recovered. In the hot chirally restored phase we find evidence for a screened interaction. The T=0 chirally symmetric phase is most readily distinguished from the symmetric phase at high T via the fermion dispersion relation.Comment: 18 page

Level Crossing for Hot Sphalerons

We study the spectrum of the Dirac Hamiltonian in the presence of high temperature sphaleron-like fluctuations of the electroweak gauge and Higgs fields, relevant for the conditions prevailing in the early universe. The fluctuations are created by numerical lattice simulations. It is shown that a change in Chern-Simons number by one unit is accompanied by eigenvalues crossing zero and a change of sign of the generalized chirality \tGf= (-1)^{2T+1} \gf which labels these modes. This provides further evidence that the sphaleron-like configurations observed in lattice simulations may be viewed as representing continuum configurations.Comment: Latex file, 29 pages + 13 figure

Diquark Condensate in QCD with Two Colors at Next-to-Leading Order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau-Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is second order.Comment: 29 pages, 2 figure

The Phases and Triviality of Scalar Quantum Electrodynamics

The phase diagram and critical behavior of scalar quantum electrodynamics are investigated using lattice gauge theory techniques. The lattice action fixes the length of the scalar (``Higgs'') field and treats the gauge field as non-compact. The phase diagram is two dimensional. No fine tuning or extrapolations are needed to study the theory's critical behovior. Two lines of second order phase transitions are discovered and the scaling laws for each are studied by finite size scaling methods on lattices ranging from $6^4$ through $24^4$. One line corresponds to monopole percolation and the other to a transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent specific heats. The lines of transitions cross in the interior of the phase diagram and appear to be unrelated. The monopole percolation transition has critical indices which are compatible with ordinary four dimensional percolation uneffected by interactions. Finite size scaling and histogram methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line are well-fit by the hypothesis that scalar quantum electrodynamics is logarithmically trivial. The logarithms are measured in both finite size scaling of the specific heat peaks as a function of volume as well as in the coupling constant dependence of the specific heats measured on fixed but large lattices. The theory is seen to be qualitatively similar to $\lambda\phi^{4}$. The standard CRAY random number generator RANF proved to be inadequateComment: 25pages,26figures;revtex;ILL-(TH)-94-#12; only hardcopy of figures availabl

Breastfeeding and motor development: A longitudinal cohort study

Background: While there is a large body of work supporting the importance of early feeding practices on cognitive, immunity, behavioural and mental outcomes, few longitudinal studies have focused on motor development. The relationship between duration of breast feeding and motor development outcomes at 10, 14, and 17 years were examined. Methods: Data were obtained from the Western Australian Pregnancy (Raine) Study. There were 2868 live births recorded and children were examined for motor proficiency at 10 (M = 10.54, SD = 2.27), 14 (M = 14.02, SD = 2.33) and 17 (M = 16.99, SD = 2.97) years using the McCarron Assessment of Neuromuscular Development (MAND). Using linear mixed models, adjusted for covariates known to affect motor development, the influence of predominant breast feeding for⩾6 months on motor development outcomes was examined. Results: Breast feeding for ⩾6 months was positively associated with improved motor development outcomes at 10, 14 and 17 years of age (p = 0.019, β 1.38) when adjusted for child’s sex, maternal age, alcohol intake, family income, hypertensive status, gestational stress and mode of delivery. Conclusion: Early life feeding practices have an influence on motor development outcomes into late childhood and adolescence independent of sociodemographic factors. Abbreviations: MAND, McCarron Assessment of Neuromuscular Development; NDI, Neuromuscular Development Index; BP, Blood Pressure; APGAR, appearance pulse, grimace, activity, respiration; SRM, spontaneous rupture of membranes; LC-PUFA, long chain polyunsaturated fatty acids; AA, arachidonic acid; DA, docosahexaenoic aci