Renormalized Vacuum Polarization and Stress Tensor on the Horizon of a Schwarzschild Black Hole Threaded by a Cosmic String

We calculate the renormalized vacuum polarization and stress tensor for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinte straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.Comment: This is an expanded version of a previous submission, we have added the calculation of the stress tensor. 28 pages, 7 figure

Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.Comment: 5 pages, 3 figure

Analytical solutions for two atoms in a harmonic trap: p-wave interactions

We derive analytical solutions for the system of two ultracold spin-polarized fermions interacting in p wave and confined in an axially symmetric harmonic trap. To this end we utilize p-wave pseudopotential with an energy-dependent scattering volume. This allows to describe the scattering in tight trapping potentials in the presence of scattering resonances. We verify predictions of the pseudopotential treatment for some model interaction potential, obtaining an excellent agreement with exact energy levels. Then we turn to the experimentally relevant case of neutral atom interactions in the vicinity of a p-wave Feshbach resonance. In the framework of the multichannel quantum-defect theory we derive relatively simple formula for an energy-dependent scattering volume, and later we apply it to investigate the energy spectrum of trapped atoms close to the p-wave Feshbach resonance.Comment: 13 pages, 5 figure

High temperature thermodynamics of strongly interacting s-wave and p-wave Fermi gases in a harmonic trap

We theoretically investigate the high-temperature thermodynamics of a strongly interacting trapped Fermi gas near either s-wave or p-wave Feshbach resonances, using a second order quantum virial expansion. The second virial coefficient is calculated based on the energy spectrum of two interacting fermions in a harmonic trap. We consider both isotropic and anisotropic harmonic potentials. For the two-fermion interaction, either s-wave or p-wave, we use a pseudopotential parametrized by a scattering length and an effective range. This turns out to be the simplest way of encoding the energy dependence of the low-energy scattering amplitude or phase shift. This treatment of the pseudopotential can be easily generalized to higher partial-wave interactions. We discuss how the second virial coefficient and thermodynamics are affected by the existence of these finite-range interaction effects. The virial expansion result for a strongly interacting s -wave Fermi gas has already been proved very useful. In the case of p-wave interactions, our results for the high-temperature equation of state are applicable to future high-precision thermodynamic measurements for a spin-polarized Fermi gas near a p-wave Feshbach resonance.Comment: 12 pages,10 figure

Monitoring collagen gelling by elastic scattering spectroscopy (ESS)

Collagen is being used extensively in tissue engineering and on a larger scale in the field of cosmetic surgery. It is either used as a gel or plastically compressed sheet. The fundamental science behind collagen gelling has been studied but little is known about the precise timing of gelling and the variables that affect gelling in the first 30 minutes. Critically, before collagen can be engineered as a predictable functional material we must be able to control fibril aggregation and gel formation. Here we report on the use of elastic scattering spectroscopy (ESS) to detect changes in scattering in rat tail and GMP bovine skin collagen during gelling. Effect of cell seeding on gelling is also reported

The self-force on a static scalar test-charge outside a Schwarzschild black hole

The finite part of the self-force on a static scalar test-charge outside a Schwarzschild black hole is zero. By direct construction of Hadamard's elementary solution, we obtain a closed-form expression for the minimally coupled scalar field produced by a test-charge held fixed in Schwarzschild spacetime. Using the closed-form expression, we compute the necessary external force required to hold the charge stationary. Although the energy associated with the scalar field contributes to the renormalized mass of the particle (and thereby its weight), we find there is no additional self-force acting on the charge. This result is unlike the analogous electrostatic result, where, after a similar mass renormalization, there remains a finite repulsive self-force acting on a static electric test-charge outside a Schwarzschild black hole. We confirm our force calculation using Carter's mass-variation theorem for black holes. The primary motivation for this calculation is to develop techniques and formalism for computing all forces - dissipative and non-dissipative - acting on charges and masses moving in a black-hole spacetime. In the Appendix we recap the derivation of the closed-form electrostatic potential. We also show how the closed-form expressions for the fields are related to the infinite series solutions.Comment: RevTeX, To Appear in Phys. Rev.

The hybrid spectral problem and Robin boundary conditions

The hybrid spectral problem where the field satisfies Dirichlet conditions (D) on part of the boundary of the relevant domain and Neumann (N) on the remainder is discussed in simple terms. A conjecture for the C_1 coefficient is presented and the conformal determinant on a 2-disc, where the D and N regions are semi-circles, is derived. Comments on higher coefficients are made. A hemisphere hybrid problem is introduced that involves Robin boundary conditions and leads to logarithmic terms in the heat--kernel expansion which are evaluated explicitly.Comment: 24 pages. Typos and a few factors corrected. Minor comments added. Substantial Robin additions. Substantial revisio

Organization specific predictors of job satisfaction: findings from a Canadian multi-site quality of work life cross-sectional survey

BACKGROUND: Organizational features can affect how staff view their quality of work life. Determining staff perceptions about quality of work life is an important consideration for employers interested in improving employee job satisfaction. The purpose of this study was to identify organization specific predictors of job satisfaction within a health care system that consisted of six independent health care organizations. METHODS: 5,486 full, part and causal time (non-physician) staff on active payroll within six organizations (2 community hospitals, 1 community hospital/long-term care facility, 1 long-term care facility, 1 tertiary care/community health centre, and 1 visiting nursing agency) located in five communities in Central West Ontario, Canada were asked to complete a 65-item quality of work life survey. The self-administered questionnaires collected staff perceptions of: co-worker and supervisor support; teamwork and communication; job demands and decision authority; organization characteristics; patient/resident care; compensation and benefits; staff training and development; and impressions of the organization. Socio-demographic data were also collected. RESULTS: Depending on the organization, between 15 and 30 (of the 40 potential predictor) variables were found to be statistically associated with job satisfaction (univariate analyses). Logistic regression analyses identified the best predictors of job satisfaction and these are presented for each of the six organizations and for all organizations combined. CONCLUSIONS: The findings indicate that job satisfaction is a multidimensional construct and although there appear to be some commonalities across organizations, some predictors of job satisfaction appear to be organization and context specific

Interaction between particles with inhomogeneous surface charge distributions: Revisiting the Coulomb fission of dication molecular clusters

An analytical solution describing the electrostatic interaction between particles with inhomogeneous surface charge distributions has been developed. For particles, each carrying a single charge, the solution equates to the presence of a point charge residing on the surface, which makes it particularly suitable for investigating the Coulomb fission of doubly charged clusters close to the Rayleigh instability limit. For a series of six separate molecular dication clusters, centre-of-mass kinetic energy releases have been extracted from experimental measurements of their kinetic energy spectra following Coulomb fission. These data have been compared with Coulomb energy barriers calculated from the electrostatic interaction energies given by this new solution. For systems with high dielectric permittivity, results from the point charge model provide a viable alternative to kinetic energy releases calculated on the assumption of a uniform distribution of surface charge. The equivalent physical picture for the clusters would be that of a trapped proton. For interacting particles with low dielectric permittivity, a uniform distribution of charge provides better agreement with the experimental results