Cold dilute neutron matter on the lattice I: Lattice virial coefficients and large scattering lengths

We study cold dilute neutron matter on the lattice using an effective field theory. We work in the unitary limit in which the scattering length is much larger than the interparticle spacing. In this paper we focus on the equation of state at temperatures above the Fermi temperature and compare lattice simulations to the virial expansion on the lattice and in the continuum. We find that in the unitary limit lattice discretization errors in the second virial coefficient are significantly enhanced. As a consequence the equation of state does not show the universal scaling behavior expected in the unitary limit. We suggest that scaling can be improved by tuning the second virial coefficient rather than the scattering length.Comment: 17 pages, 12 figure

Volume Dependence of Bound States with Angular Momentum

We derive general results for the mass shift of bound states with angular momentum l >= 1 in a finite periodic volume. Our results have direct applications to lattice simulations of hadronic molecules as well as atomic nuclei. While the binding of S-wave bound states increases at finite volume, we show that the binding of P-wave bound states decreases. The mass shift for D-wave bound states as well as higher partial waves depends on the representation of the cubic rotation group. Nevertheless, the multiplet-averaged mass shift for any angular momentum l can be expressed in a simple form, and the sign of the shift alternates for even and odd l. We verify our analytical results with explicit numerical calculations. We also show numerically that similar volume corrections appear in three-body bound states.Comment: 4 pages, 3 figures, final versio

Diffusion of active tracers in fluctuating fields

The problem of a particle diffusion in a fluctuating scalar field is studied. In contrast to most studies of advection diffusion in random fields we analyze the case where the particle position is also coupled to the dynamics of the field. Physical realizations of this problem are numerous and range from the diffusion of proteins in fluctuating membranes and the diffusion of localized magnetic fields in spin systems. We present exact results for the diffusion constant of particles diffusing in dynamical Gaussian fields in the adiabatic limit where the field evolution is much faster than the particle diffusion. In addition we compute the diffusion constant perturbatively, in the weak coupling limit where the interaction of the particle with the field is small, using a Kubo-type relation. Finally we construct a simple toy model which can be solved exactly.Comment: 13 pages, 1 figur

Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

High-spin intruder states in the fp shell nuclei and isoscalar proton-neutron correlations

We perform a systematic shell-model and mean-field study of fully-aligned, high-spin f_{7/2}^{n} seniority isomers and d_{3/2}^{-1} f_{7/2}^{n+1} intruder states in the A~44 nuclei from the lower-fp shell. The shell-model calculations are performed in the full sdfp configuration space allowing 1p-1h cross-shell excitations. The self-consistent mean-field calculations are based on the Hartree-Fock approach with the Skyrme energy density functional that reproduces empirical Landau parameters. While there is a nice agreement between experimental and theoretical relative energies of fully-aligned states in N>Z nuclei, this is no longer the case for the N=Z systems. The remaining deviation from the data is attributed to the isoscalar proton-neutron correlations. It is also demonstrated that the Coulomb corrections at high spins noticeably depend on the choice of the energy density functional.Comment: 4 pages. submitted to Phys. Rev. Let

Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.Comment: 18 pages, 4 figures .eps, JPA styl

A Risk Comparison of Ordinary Least Squares vs Ridge Regression

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method is within a constant factor (namely 4) of the risk of ridge regression.Comment: Appearing in JMLR 14, June 201

Do Individual Differences And Aging Effects In The Estimation Of Geographical Slant Reflect Cognitive Or Perceptual Effects?

Several individual differences including age have been suggested to affect the perception of slant. A cross-sectional study of outdoor hill estimation (N = 106) was analyzed using individual difference measures of age, experiential knowledge, fitness, personality traits, and sex. Of particular note, it was found that for participants who reported any experiential knowledge about slant, estimates decreased (i.e., became more accurate) as conscientiousness increased, suggesting that more conscientious individuals were more deliberate about taking their experiential knowledge (rather than perception) into account. Effects of fitness were limited to those without experiential knowledge, suggesting that they, too, may be cognitive rather than perceptual. The observed effects of age, which tended to produce lower, more accurate estimates of hill slant, provide more evidence that older adults do not see hills as steeper. The main effect of age was to lower slant estimates; such effects may be due to implicit experiential knowledge acquired over a lifetime. The results indicate the impact of cognitive, rather than perceptual factors on individual differences in slant estimation

ω-3 LCPUFA supplementation during pregnancy and risk of allergic outcomes or sensitization in offspring: A systematic review and meta-analysis

Background: Allergic diseases have increased worldwide in the last 2 decades, with children suffering the highest burden of the condition. The ω-3 long-chain poly-unsaturated fatty acid (LCPUFA) possesses anti-inflammatory properties that could lead to a reduction in inflammatory mediators in allergies. Objective: A systematic review and meta-analysis of the most recent follow-ups of randomized clinical trials (RCTs) was conducted to assess the effectiveness of ω-3 LCPUFA supplementation started during pregnancy on allergic outcomes in offspring. Methods: The RCTs with a minimum of 1-month follow-up post gestation were eligible for inclusion. The CENTRAL, MEDLINE, SCOPUS, WHO's International Clinical Trials Register, E-theses, and Web of Science databases were searched. Study quality was evaluated using the Cochrane Collaboration's risk of bias tool. Results: Ten RCTs (3,637 children), from 9 unique trials, examined the effectiveness of ω-3 LCPUFA supplementation started during pregnancy on the development of allergic outcomes in offspring. Heterogeneities were seen between the trials in terms of their sample, type, and duration of intervention and follow-up. Pooled estimates showed a significant reduction in childhood “sensitization to egg” (relative risk [RR] = 0.54, 95% confidence interval [CI] = 0.32-0.90), and “sensitization to peanut” (RR = 0.62, 95% CI = 0.40-0.96). No statistical differences were found for other allergic outcomes (eg, eczema, asthma/wheeze). Conclusion: These results suggest that intake of ω-3 LCPUFA started during pregnancy can reduce the risk of sensitization to egg and peanut; however, the evidence is limited because of the small number of studies that contributed to the meta-analyses. The current evidence on the association between supplementation with ω-3 LCPUFA started during pregnancy and allergic outcomes is weak, because of the risk of bias and heterogeneities between studies