A Quantum Mechanical Model of Spherical Supermembranes

We present a quantum mechanical model of spherical supermembranes. Using superfields to represent the cartesian coordinates of the membrane, we are able to exactly determine its supersymmetric vacua. We find there are two classical vacua, one corresponding to an extended membrane and one corresponding to a point-like membrane. For the ${\mathcal N} = 2$ case, instanton effects then lift these vacua to massive states. For the ${\mathcal N} = 4$ case, there is no instanton tunneling, and the vacua remain massless. Similarities to spherical supermembranes as giant gravitons and in Matrix theory on pp-waves is discussed.Comment: 9 page

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

DD-dimensions Dirac fermions BEC-BCS cross-over thermodynamics

An effective Proca Lagrangian action is used to address the vector condensation Lorentz violation effects on the equation of state of the strongly interacting fermions system. The interior quantum fluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized Thomson Problem counterterm background. The general analytical formulas for the $d$-dimensions thermodynamics are given near the unitary limit region. In the non-relativistic limit for $d=3$, the universal dimensionless coefficient $\xi ={4}/{9}$ and energy gap $\Delta/\epsilon_f ={5}/{18}$ are reasonably consistent with the existed theoretical and experimental results. In the unitary limit for $d=2$ and T=0, the universal coefficient can even approach the extreme occasion $\xi=0$ corresponding to the infinite effective fermion mass $m^*=\infty$ which can be mapped to the strongly coupled two-dimensions electrons and is quite similar to the three-dimensions Bose-Einstein Condensation of ideal boson gas. Instead, for $d=1$, the universal coefficient $\xi$ is negative, implying the non-existence of phase transition from superfluidity to normal state. The solutions manifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.Comment: Improved versio

Nab: Measurement Principles, Apparatus and Uncertainties

The Nab collaboration will perform a precise measurement of 'a', the electron-neutrino correlation parameter, and 'b', the Fierz interference term in neutron beta decay, in the Fundamental Neutron Physics Beamline at the SNS, using a novel electric/magnetic field spectrometer and detector design. The experiment is aiming at the 10^{-3} accuracy level in (Delta a)/a, and will provide an independent measurement of lambda = G_A/G_V, the ratio of axial-vector to vector coupling constants of the nucleon. Nab also plans to perform the first ever measurement of 'b' in neutron decay, which will provide an independent limit on the tensor weak coupling.Comment: 12 pages, 6 figures, 1 table, talk presented at the International Workshop on Particle Physics with Slow Neutrons, Grenoble, 29-31 May 2008; to appear in Nucl. Instrum. Meth. in Physics Research

The association between blood metals and hypertension in the GuLF study

Background: Both essential and non-essential metals come from natural and anthropogenic sources. Metals can bioaccumulate in humans and may impact human health, including hypertension. Methods: Blood metal (cadmium, lead, mercury, manganese, and selenium) concentrations were measured at baseline for a sample of participants in the Gulf Long-Term Follow-up (GuLF) Study. The GuLF Study is a prospective cohort study focused on potential health effects following the 2010 Deepwater Horizon oil spill. Hypertension was defined as high systolic (≥140 mm Hg) or diastolic (≥90 mm Hg) blood pressure or taking anti-hypertensive medications. A total of 957 participants who had blood measurement for at least one metal, baseline blood pressure measurements, information on any anti-hypertensive medication use, and relevant covariates were included in this cross-sectional analysis. We used Poisson regression to explore the association between individual blood metal levels and hypertension. Quantile-based g-computation was used to investigate the association between the metal mixture and hypertension. We also explored the association between individual blood metal levels and continuous blood pressure measurements using general linear regression. Results: Comparing the highest quartile of blood metals with the lowest (Q4vs1), the hypertension prevalence ratio (PR) was 0.92 (95 % confidence interval (CI) = 0.73,1.15) for cadmium, 0.86 (95%CI = 0.66,1.12) for lead, 0.89 (95%CI = 0.71,1.12) for mercury, 1.00 (95%CI = 0.80,1.26) for selenium, and 1.22 (95%CI = 0.95,1.57) for manganese. We observed some qualitative differences across race and BMI strata although none of these differences were statistically significant. In stratified analyses, the PR (Q4vs1) for mercury was 0.69 (95%CI = 0.53, 0.91) in White participants and 1.29 (95%CI = 0.86,1.92) in Black participants (p for interaction = 0.5). The PR (Q4vs1) for manganese was relatively higher in Black participants (PR = 1.37, 95%CI = 0.92,2.05) than in White participants (PR = 1.15, 95%CI = 0.83,1.60, p for interaction = 0.5), with a suggestive dose-response among Blacks. After stratifying by obesity (BMI ≥30 and < 30), positive associations of of hypertension with cadmium (PR [Q4vs1] = 1.19, 95%CI = 0.91,1.56, p for interaction = 0.5), lead (PR [Q4vs1] = 1.14, 95%CI = 0.84,1.55, p for interaction = 1.0) and manganese (PR = 1.25, 95%CI = 0.93,1.68, p for interaction = 0.8) were observed in participants with BMI≥30, but not in participants with BMI<30. The joint effect of the metal mixture was 0.96 (95%CI = 0.73,1.27). We did not observe clear associations between blood metal levels and continuous blood pressure measurements. Conclusion: We did not find overall cross-sectional associations between blood cadmium, lead, mercury, selenium levels and hypertension or blood pressure. We found some evidence suggesting that manganese might be positively associated with risk of hypertension. Associations varied somewhat by race and BMI

Twist-2 Heavy Flavor Contributions to the Structure Function g2(x,Q2)g_2(x,Q^2)

The twist--2 heavy flavor contributions to the polarized structure function $g_2(x,Q^2)$ are calculated. We show that this part of $g_2(x,Q^2)$ is related to the heavy flavor contribution to $g_1(x,Q^2)$ by the Wandzura--Wilczek relation to all orders in the strong coupling constant. Numerical results are presented.Comment: 17 pages LATEX, 1 style files, 4 figure

CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form $a(\eta)=c_1\eta^2+c_2\eta+c_3$, where $c_i$ are constants. During the mixed phase the universe smoothly transforms from being radiation to dust dominated. We find analytic expressions for the graviton mode function during the mixed phase in terms of spheroidal wave functions. This mode function is used to find an analytic expression for the multipole moments $\langle a_l^2\rangle$ of the two-point angular correlation function $C(\gamma)$ for the CBR anisotropy. The analytic expression for the multipole moments is written in terms of two integrals, which are evaluated numerically. The results are compared to multipoles calculated for models that are {\it completely} dust dominated at last-scattering. We find that the multipoles $\langle a_l^2\rangle$ of the CBR temperature perturbations for $l>10$ are significantly larger for a universe that contains both radiation and dust at last-scattering. We compare our results with recent, similar numerical work and find good agreement. The spheroidal wave functions may have applications to other problems of cosmological interest.Comment: 28 pgs + 6 postscript figures, RevTe

Bifurcation and stability for Nonlinear Schroedinger equations with double well potential in the semiclassical limit

We consider the stationary solutions for a class of Schroedinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give the stationary solutions, up to an exponentially small term, and that symmetry-breaking bifurcation occurs at a given value for the strength of the nonlinear term. The kind of bifurcation picture only depends on the non-linearity power. We then discuss the stability/instability properties of each branch of the stationary solutions. Finally, we consider an explicit one-dimensional toy model where the double well potential is given by means of a couple of attractive Dirac's delta pointwise interactions.Comment: 46 pages, 4 figure