Cosmological and Black Hole Horizon Fluctuations

The quantum fluctuations of horizons in Robertson-Walker universes and in the Schwarzschild spacetime are discussed. The source of the metric fluctuations is taken to be quantum linear perturbations of the gravitational field. Lightcone fluctuations arise when the retarded Green's function for a massless field is averaged over these metric fluctuations. This averaging replaces the delta-function on the classical lightcone with a Gaussian function, the width of which is a measure of the scale of the lightcone fluctuations. Horizon fluctuations are taken to be measured in the frame of a geodesic observer falling through the horizon. In the case of an expanding universe, this is a comoving observer either entering or leaving the horizon of another observer. In the black hole case, we take this observer to be one who falls freely from rest at infinity. We find that cosmological horizon fluctuations are typically characterized by the Planck length. However, black hole horizon fluctuations in this model are much smaller than Planck dimensions for black holes whose mass exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations which are sufficiently small as not to invalidate the semiclassical derivation of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps

Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps

A Search for Hard X-Ray Emission from Globular Clusters - Constraints from BATSE

We have monitored a sample of 27 nearby globular clusters in the hard X-ray band (20-120 keV) for approximately 1400 days using the BATSE instrument on board the Compton Gamma-Ray Observatory. Globular clusters may contain a large number of compact objects (e.g., pulsars or X-ray binaries containing neutron stars) which can produce hard X-ray emission. Our search provides a sensitive (~50 mCrab) monitor for hard X-ray transient events on time scales of >1 day and a means for observing persistent hard X-ray emission. We have discovered no transient events from any of the clusters and no persistent emission. Our observations include a sensitive search of four nearby clusters containing dim X-ray sources: 47 Tucanae, NGC 5139, NGC 6397, and NGC 6752. The non-detection in these clusters implies a lower limit for the recurrence time of transients of 2 to 6 years for events with luminosities >10^36 erg s^-1 (20-120 keV) and ~20 years if the sources in these clusters are taken collectively. This suggests that the dim X-ray sources in these clusters are not transients similar to Aql~X-1. We also place upper limits on the persistent emission in the range 2-10*10^34 erg s^-1 (2 sigma, 20-120 keV) for these four clusters. For 47 Tuc the upper limit is more sensitive than previous measurements by a factor of 3. We find a model dependent upper limit of 19 isolated millisecond pulsars (MSPs) producing gamma-rays in 47 Tuc, compared to the 11 observed radio MSPs in this cluster.Comment: 20 pages; accepted, ApJ; uu encoded tar file; 7 figure

Minimum target prices for production of direct acting antivirals and associated diagnostics to combat Hepatitis C Virus

Combinations of direct-acting antivirals (DAAs) can cure hepatitis C virus (HCV) in the majority of treatment-naïve patients. Mass treatment programs to cure HCV in developing countries are only feasible if the costs of treatment and laboratory diagnostics are very low. This analysis aimed to estimate minimum costs of DAA treatment and associated diagnostic monitoring. Clinical trials of HCV DAAs were reviewed to identify combinations with consistently high rates of sustained virological response across hepatitis C genotypes. For each DAA, molecular structures, doses, treatment duration, and components of retrosynthesis were used to estimate costs of large-scale, generic production. Manufacturing costs per gram of DAA were based upon treating at least 5 million patients per year and a 40% margin for formulation. Costs of diagnostic support were estimated based on published minimum prices of genotyping, HCV antigen tests plus full blood count/clinical chemistry tests. Predicted minimum costs for 12-week courses of combination DAAs with the most consistent efficacy results were: US$122 per person for sofosbuvir+daclatasvir; US$152 for sofosbuvir+ribavirin; US$192 for sofosbuvir+ledipasvir; and US$115 for MK-8742+MK-5172. Diagnostic testing costs were estimated at US$90 for genotyping US$34 for two HCV antigen tests and US$22 for two full blood count/clinical chemistry tests. Conclusions: Minimum costs of treatment and diagnostics to cure hepatitis C virus infection were estimated at US$171-360 per person without genotyping or US$261-450 per person with genotyping. These cost estimates assume that existing large-scale treatment programs can be established. (Hepatology 2015;61:1174–1182

Measured quantum probability distribution functions for Brownian motion

The quantum analog of the joint probability distributions describing a classical stochastic process is introduced. A prescription is given for constructing the quantum distribution associated with a sequence of measurements. For the case of quantum Brownian motion this prescription is illustrated with a number of explicit examples. In particular it is shown how the prescription can be extended in the form of a general formula for the Wigner function of a Brownian particle entangled with a heat bath.Comment: Phys. Rev. A, in pres

Nevirapine-Induced Heratotoxicity: Incidence, Risk Factors and Associated Mortality in a Primary Care ART Programme in South Africa

CROI 200

Quantum inequalities for the free Rarita-Schwinger fields in flat spacetime

Using the methods developed by Fewster and colleagues, we derive a quantum inequality for the free massive spin-${3\over 2}$ Rarita-Schwinger fields in the four dimensional Minkowski spacetime. Our quantum inequality bound for the Rarita-Schwinger fields is weaker, by a factor of 2, than that for the spin-${1\over 2}$ Dirac fields. This fact along with other quantum inequalities obtained by various other authors for the fields of integer spin (bosonic fields) using similar methods lead us to conjecture that, in the flat spacetime, separately for bosonic and fermionic fields, the quantum inequality bound gets weaker as the the number of degrees of freedom of the field increases. A plausible physical reason might be that the more the number of field degrees of freedom, the more freedom one has to create negative energy, therefore, the weaker the quantum inequality bound.Comment: Revtex, 11 pages, to appear in PR

Quantum corrected geodesics

We compute the graviton-induced corrections to the trajectory of a classical test particle. We show that the motion of the test particle is governed by an effective action given by the expectation value (with respect to the graviton state) of the classical action. We analyze the quantum corrected equations of motion for the test particle in two particular backgrounds: a Robertson Walker spacetime and a 2+1 dimensional spacetime with rotational symmetry. In both cases we show that the quantum corrected trajectory is not a geodesic of the background metric.Comment: LaTeX file, 15 pages, no figure

On a hybrid fourth moment involving the Riemann zeta-function

We provide explicit ranges for $\sigma$ for which the asymptotic formula \begin{equation*} \int_0^T|\zeta(1/2+it)|^4|\zeta(\sigma+it)|^{2j}dt \;\sim\; T\sum_{k=0}^4a_{k,j}(\sigma)\log^k T \quad(j\in\mathbb N) \end{equation*} holds as $T\rightarrow \infty$, when $1\leq j \leq 6$, where $\zeta(s)$ is the Riemann zeta-function. The obtained ranges improve on an earlier result of the authors [Annales Univ. Sci. Budapest., Sect. Comp. {\bf38}(2012), 233-244]. An application to a divisor problem is also givenComment: 21 page