Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients

Casimir energy is a nonlocal effect; its magnitude cannot be deduced from heat kernel expansions, even those including the integrated boundary terms. On the other hand, it is known that the divergent terms in the regularized (but not yet renormalized) total vacuum energy are associated with the heat kernel coefficients. Here a recent study of the relations among the eigenvalue density, the heat kernel, and the integral kernel of the operator $e^{-t\sqrt{H}}$ is exploited to characterize this association completely. Various previously isolated observations about the structure of the regularized energy emerge naturally. For over 20 years controversies have persisted stemming from the fact that certain (presumably physically meaningful) terms in the renormalized vacuum energy density in the interior of a cavity become singular at the boundary and correlate to certain divergent terms in the regularized total energy. The point of view of the present paper promises to help resolve these issues.Comment: 19 pages, RevTeX; Discussion section rewritten in response to referees' comments, references added, minor typos correcte

Correlations around an interface

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures.Comment: RevTeX, 13 pages, 6 figure

Geothermal Casimir Phenomena

We present first worldline analytical and numerical results for the nontrivial interplay between geometry and temperature dependencies of the Casimir effect. We show that the temperature dependence of the Casimir force can be significantly larger for open geometries (e.g., perpendicular plates) than for closed geometries (e.g., parallel plates). For surface separations in the experimentally relevant range, the thermal correction for the perpendicular-plates configuration exhibits a stronger parameter dependence and exceeds that for parallel plates by an order of magnitude at room temperature. This effect can be attributed to the fact that the fluctuation spectrum for closed geometries is gapped, inhibiting the thermal excitation of modes at low temperatures. By contrast, open geometries support a thermal excitation of the low-lying modes in the gapless spectrum already at low temperatures.Comment: 8 pages, 3 figures, contribution to QFEXT07 proceedings, v2: discussion switched from Casimir energy to Casimir force, new analytical results included, matches JPhysA versio

Trends in U.S. Public Awareness of Racial and Ethnic Health Disparities (1999-2010): 2009 General Population Toplines

Not provided

Trends in U.S. Public Awareness of Racial and Ethnic Health Disparities (1999-2010): Study Brief

None provided

Numerical Simulation of an Electroweak Oscillon

Numerical simulations of the bosonic sector of the $SU(2)\times U(1)$ electroweak Standard Model in 3+1 dimensions have demonstrated the existence of an oscillon -- an extremely long-lived, localized, oscillatory solution to the equations of motion -- when the Higgs mass is equal to twice the $W^\pm$ boson mass. It contains total energy roughly 30 TeV localized in a region of radius 0.05 fm. A detailed description of these numerical results is presented.Comment: 12 pages, 8 figures, uses RevTeX4; v2: expanded results section, fixed typo

Emergence of Oscillons in an Expanding Background

We consider a (1+1) dimensional scalar field theory that supports oscillons, which are localized, oscillatory, stable solutions to nonlinear equations of motion. We study this theory in an expanding background and show that oscillons now lose energy, but at a rate that is exponentially small when the expansion rate is slow. We also show numerically that a universe that starts with (almost) thermal initial conditions will cool to a final state where a significant fraction of the energy of the universe -- on the order of 50% -- is stored in oscillons. If this phenomenon persists in realistic models, oscillons may have cosmological consequences.Comment: 13 pages, 4 .eps figures, uses RevTeX4; v2: clarified details of expansion, added reference

Fronts and interfaces in bistable extended mappings

We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the convolution with a function of bounded variation. We prove the existence of travelling wave interfaces, namely fronts, and the uniqueness of the corresponding selected velocity and shape. This selected velocity is shown to be the propagating velocity for any interface, to depend continuously on the couplings and to increase with the symmetry parameter of the local nonlinearity. We apply the results to several examples including discrete and continuous couplings, and the planar fronts' dynamics in multi-dimensional Coupled Map Lattices. We eventually emphasize on the extension to other kinds of fronts and to a more general class of bistable extended mappings for which the couplings are allowed to be nonlinear and the local map to be smooth.Comment: 27 pages, 3 figures, submitted to Nonlinearit

A Meta-Analytic Review of Achievement Goal Orientation Correlates in Competitive Sport: A Follow-Up to Lochbaum et al. (2016)

Recent quantitative research in competitive sport with the Task and Ego Orientations in Sport Questionnaire (TEOSQ) and Perceptions of Success Questionnaire (POSQ) pointed to a potential critical issue that the two questionnaires did not agree across a number tested hypotheses (Lochbaum, Kazak Çetinkalp, Graham, Wright, & Zazo, 2016). Thus, the present quantitative review examined whether correlates of the two achievement goal orientations were moderated by the two measures. To achieve this purpose, 772 unique correlates (489 TEOSQ, 283 POSQ; 402 task orientation, 370 ego orientation) from 93 studies spanning 1989-2016 from 32 countries with 26,387 participants were placed into 15 different categories and meta-analyzed. The task goal orientation was significantly and small to moderate in meaningfulness related to adaptive success factors (rw=.29), maladaptive success factors (rw=-.12), desirable behaviors (rw=.28), positive emotions (rw=.35), amotivation (rw=-.13), extrinsic motivation (rw=.20), external regulations (rw=.12), internal regulations (rw=.34), intrinsic motivation (rw=.47), the mastery/task climate (rw=.38), perceived competence (rw=.26), and trait selfesteem (rw=.35). The ego goal orientation was significantly and small in meaningfulness related to adaptive success factors (rw=.10), maladaptive success factors (rw=.12), negative emotions (rw=.11), undesirable behaviors (rw=.23), amotivation (rw=.16), extrinsic motivation (rw=.28), external regulation (rw=.21), intrinsic motivation (rw=.14), performance/ego climate (rw=.28), and perceived competence (rw=.17). The questionnaire measure was a significant moderator for the task goal orientation relationship with desirable behaviors (POSQ rw=.24; TEOSQ rw=.37), internal regulations (POSQ rw=.26; TEOSQ rw=.39), and trait self-esteem (POSQ rw=.45; TEOSQ rw=.32) and for the ego goal orientation relationship with performance/ego climate (POSQ rw=.34; TEOSQ rw=.24). Overall, the extent of the questionnaire type being a concern when examining correlates was fortunately minimal. Yet, differences in the two dominant measures exit. Recommendations for future research examining both the TEOSQ and POSQ were proposed