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Polarization of a vacuum as well as of dispersive and dissipative dielectric media with piece-wise and smooth inhomogeneities is studied with the goal to clarify the question of renormalizability of diverging electromagnetic stress-energy tensor. First, the stress tensor is computed with the Lifshitz approach to London forces in the non-retarded limit, which after the substraction of the leading free space ultraviolet divergencies still retains the divergencies associated with the presence of sharp boundaries between piece-wise inhomogeneities. We call these contributions finite because they become renormalized after a sharp interface is replaced with a dielectric permittivity changing according to a smooth function of spatial coordinates. In addition, such a smoothed out interface exhibits new subleading ultraviolet divergencies that appear due to its internal structure. To systematically deal with the polarization of inhomogeneous media, the Hadamard expansion is applied to single out both finite and subleading contributions and to unequivocally demonstrate incomplete renormalizability of the Lifshitz theory. The above approach also allows us to reveal the nature of surface tension, which proves to be purely quantum mechanical. The deduced theory of surface tension and its calculations for real dielectric media are favorably compared to the available experimental data. While the sharp interface limit recovers the classical boundary conditions for the electric field and uncovers the origin of the apparent local divergencies of the renormalized stresses in the sharp interface formulation previously pointed out in the literature, the problem of surface tension proves to be of a distinguished limit type because the sharp interface formulation loses the information about the internal structure of an interface and hence cannot explain the origin of surface tension. Comment: 62 pages, 7 figures

Real spherical designs and real and complex projective designs have been shown by Delsarte, Goethals, and Seidel to give rise to association schemes when the strength of the design is high compared to its degree as a code. In contrast, designs on the complex unit sphere remain relatively uninvestigated, despite their importance in numerous applications. In this paper we develop the notion of a complex spherical design and show how many such designs carry the structure of an association scheme. In contrast with the real spherical designs and the real and complex projective designs, these association schemes are nonsymmetric. Comment: 45 pages, no figures

We study the prime number race for elliptic curves over the function field of a proper, smooth and geometrically connected curve over a finite field. This constitutes a function field analogue of prior work by Mazur, Sarnak and the second author. In this geometric setting we can prove unconditional results whose counterparts in the number field case are conditional on a Riemann Hypothesis and a linear independence hypothesis on the zeros of the implied L-functions. Notably we show that in certain natural families of elliptic curves, the bias generically dissipates as the conductor grows. This is achieved by proving a central limit theorem and combining it with generic linear independence results that will appear in a separate paper. Also we study in detail a particular family of elliptic curves that have been considered by Ulmer. In contrast to the generic case we show that the race exhibits very diverse outcomes, some of which are believed to be impossible in the number field setting. Such behaviors are possible in the function field case because the zeros of Hasse-Weil L-functions for those elliptic curves can be proven to be highly dependent among themselves, which is a very non generic situation.

We propose the existence of an infinite-parameter family of solutions in AdS that oscillate on any number of non-commensurate frequencies. Some of these solutions appear stable when perturbed, and we suggest that they can be used to map out the AdS "islands of stability". By numerically constructing two-frequency solutions and exploring their parameter space, we find that both collapse and non-collapse are generic scenarios near AdS. Unlike other approaches, our results are valid on any timescale and do not rely on perturbation theory.

We express the entropy of a scalar field phi directly in terms of its spacetime correlation function W(x,y) = , assuming that the higher correlators are of "Gaussian" form. The resulting formula associates an entropy S(R) to any spacetime region R; and when R is globally hyperbolic with Cauchy surface Sigma, S(R) can be interpreted as the entropy of the reduced density-matrix belonging to Sigma. One acquires in particular a new expression for the entropy of entanglement across an event-horizon. Thanks to its spacetime character, this expression makes sense in a causal set as well as in a continuum spacetime. Comment: plainTeX, 14 pages, 2 figures. To appear in proceedings of ICGC2011, held Goa, Journal of Physics Conference Series. Most current version is available at http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/ (or wherever my home-page may be, such as http://www.physics.syr.edu/~sorkin/some.papers/)

AbstractBackgroundCoronavirus disease 2019 (COVID-19), caused by the novel coronavirus SARS-CoV-2, has led to significant global mortality and morbidity. Until now, no treatment has proven to be effective in COVID-19. To explore whether the use of remdesivir, initially an experimental broad-spectrum antiviral, is effective in the treatment of hospitalized patients with COVID-19, we conducted a systematic review and meta-analysis of randomized, placebo-controlled trials investigating its use.MethodsA rapid search of the MEDLINE and EMBASE medical databases was conducted for randomized controlled trials. A systematic approach was used to screen, abstract, and critically appraise the studies. Grading of Recommendations Assessment, Development, and Evaluation (GRADE) method was applied to rate the certainty and quality of the evidence reported per study.ResultsTwo RCTs studies were identified (n=1,299). A fixed-effects meta-analysis revealed reductions in mortality (RR=0.69, 0.49 to 0.99), time to clinical improvement (3.95 less days, from 3.86 days less to 4.05 less days), serious adverse events (RR=0.77, 0.63 to 0.94) and all adverse events (RR=0.87, 0.79 to 0.96).ConclusionIn this rapid systematic review, we present pooled evidence from the 2 included RCT studies that reveal that remdesivir has a modest yet significant reduction in mortality and significantly improves the time to recovery, as well as significantly reduced risk in adverse events and serious adverse events. It is more than likely that as an antiviral, remdesivir is not sufficient on its own and may be suitable in combination with other antivirals or treatments such as convalescent plasma. Research is ongoing to clarify and contextual these promising findings.

The gauged $U(1)_{L_\mu-L_\tau}$ extension of the Standard Model is a very simple framework that can alleviate the tension in muon anomalous magnetic dipole moment, reinforced by the recent Fermilab measurement. We explore experimental probes of the $(g-2)_\mu$ target with a general treatment of kinetic mixing between the $Z'$ gauge boson and the photon. The physical value of the kinetic mixing depends on a free parameter of the model and energy scale of a process. We find neutrino constraints on the $(g-2)_\mu$ target including Borexino, CE$\nu$NS, and white dwarfs are sensitive to this freedom and can be lifted if the kinetic mixing lies in proximity of zero at low momentum transfer. As a further step, we explore $L_\mu-L_\tau$ charged dark matter with a thermal origin and show that the same scenario of kinetic mixing can relax existing direct detection constraints and predict novel recoil energy dependence in the upcoming searches. Future joint effort of neutrino and dark matter experiments and precision spectral measurement will be the key to test such a theory. Comment: 25 pages, 11 figures

Context. SuperclusterA in the extragalactic HII region NGC2363 is remarkable for the hypersonic gas seen as faint extended broad emission lines with a full width zero intensity of 7000km/s. Aims. We explore the possibility that the observed broad profiles are the result of the interaction of a high velocity cluster wind with dense photoionized clumps. Methods. The geometry considered is that of near static photoionized condensations at the surface of which turbulent mixing layers arise as a result of the interaction with the hot wind. The approximative treatment of turbulence is carried out using the mixing length approach of Canto & Raga. The code mappings Ic is used to derive the mean quantities describing the flow and to compute the line emissivities within the turbulent layers. The velocity projection in three dimensions of the line sources is carried out analytically. Results. A fast entraining wind of up to ~4300km/s appears to be required to reproduce the faint wings of the broad H-alpha and [O III] profiles. A slower wind of 3500km/s, however, can still reproduce the bulk of the broad component and does provide a better fit than an ad hoc Gaussian profile. Conclusions. Radial acceleration in 3D (away from supercluster A) of the emission gas provides a reasonable first order fit to the broad line component. No broad component is predicted for the [N II] and [S II] lines, as observed. The wind velocity required is uncomfortably high and alternative processes that would provide comparable constant acceleration of the emission gas up to 4000km/s might have to be considered. Comment: 12 pages, 9 figures, accepted in A&A on 6th of March 2009, figure captions have been shortened, typos corrected

This paper analyzes third-degree price discrimination of a monopoly airline in the presence of congestion externality when all markets are served. The model features the business-passenger and leisure-passenger markets where business passengers exhibit a higher time valuation, and a less price-elastic demand, than leisure passengers. Our main result is the identification of the time-valuation effect of price discrimination, which can work in the opposite direction as the well-known output effect on welfare. This time-valuation effect clearly explains why discriminating prices can improve welfare even when this is associated with a reduction in aggregate output.

We present the results of structural and magnetic phase comparisons of the iron oxychalcogenides La$_{2}$O$_{2}$Fe$_{2}$O$M$$_{2}$ ($M$ = S, Se). Elastic neutron scattering reveals that $M$ = S and Se have similar nuclear structures at room and low temperatures. We find that both materials obtain antiferromagnetic ordering at a Neel temperature $T_{N}$ 90.1 $\pm$ 0.16 K and 107.2 $\pm$ 0.06 K for $M$= Se and S, respectively. The magnetic arrangements of $M$ = S, Se are obtained through Rietveld refinement. We find the order parameter exponent $\beta$ to be 0.129 $\pm$ 0.006 for $M$ = Se and 0.133 $\pm$ 0.007 for $M$ = S. Each of these values is near the Ising symmetry value of 1/8. This suggests that although lattice and electronic structural modifications result from chalcogen exchange, the nature of the magnetic interactions is similar in these materials.