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

Conductance Phases in Aharonov-Bohm Ring Quantum Dots

The regimes of growing phases (for electron numbers N~0-8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by the Weizmann group are accounted for by an elementary Green function formalism, appropriate to an equi-spaced ladder structure (with at least three rungs) of electronic levels in the quantum dot. The key features of the theory are physically a dissipation rate that increases linearly with the level number (and tentatively linked to coupling to longitudinal optical phonons) and a set of Fano-like meta-stable levels, which disturb the unitarity, and mathematically the change over of the position of the complex transmission amplitude-zeros from the upper-half in the complex gap-voltage plane to the lower half of that plane. The two regimes are identified with (respectively) the Blaschke-term and the Kramers-Kronig integral term in the theory of complex variables.Comment: 20 pages, 4 figure

Effects of bovine serum albumin on light activated antimicrobial surfaces

Bovine serum albumin (BSA) is currently recommended as an interfering substance to emulate organic soiling, in evaluating the efficacy of disinfectants. The European Standard recommends 0.03% BSA to test clean conditions and 0.3% for dirty conditions. Reactive oxygen species are known to exert excellent antimicrobial activity with low specificity against a broad range of pathogens. Herein, we present our data from the first study of the effects of the addition of BSA on the antibacterial activity of light activated antimicrobial surfaces. Light activated antimicrobial surfaces were made from polyurethane swell-encapsulated with gold nanoparticles (AuNPs) coated with the light active triarylmethane dye, crystal violet (PU-AuNP-CV). The antibacterial efficacy of the antimicrobial substrates was tested against two strains of Staphylococcus aureus 8325-4, a well-characterised laboratory strain and MRSA 4742, a recent clinical isolate, in the presence of 0.1% to 1% BSA by irradiating the substrates with a fluorescent lamp (300 lux). After 6 hours of irradiation, the number of surviving bacteria was determined. The results showed that BSA reduced the antibacterial efficacy of all the PU-AuNP-CV surfaces with increasing BSA concentrations resulting in a progressive reduction in antibacterial activity towards the bacteria tested. However, the light activated surfaces did perform well at 0.1 and 0.25% BSA levels, showing they may have potential for real world environments with low levels of organic soiling

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

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