Construction and analysis of a simplified many-body neutrino model

In dense neutrino systems, such as found in the early Universe, or near a supernova core, neutrino flavor evolution is affected by coherent neutrino-neutrino scattering. It has been recently suggested that many-particle quantum entanglement effects may play an essential role in these systems, potentially invalidating the traditional description in terms of a set of single-particle evolution equations. We model the neutrino system by a system of interacting spins, following an earlier work which showed that such a spin system can in some cases be solved exactly. We extend this work by constructing an exact analytical solution to a more general spin system, including initial states with asymmetric spin distribution and, moreover, not necessarily aligned along the same axis. Our solution exhibits a rich set of behaviors, including coherent oscillations and dephasing and a transition from the classical to quantum regimes. We argue that the classical evolution of the spin system captures the entire coherent behavior of the neutrino system, while the quantum effects in the spin system capture some, but not all, of the neutrino incoherent evolution. By comparing the spin and neutrino systems, we find no evidence for the violation of the accepted one-body description, though the argument involves some subtleties not appreciated before. The analysis in this paper may apply to other two-state systems beyond the neutrino field.Comment: 22 pages, 7 figure

Approximating the monomer-dimer constants through matrix permanent

The monomer-dimer model is fundamental in statistical mechanics. However, it is #P-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is proposed in this paper, by transforming the number of all matchings of a bipartite graph into the number of perfect matchings of an extended bipartite graph, which can be given by a matrix permanent. Sequential importance sampling algorithm is applied to compute the permanents. For two-dimensional lattice with periodic condition, we obtain $0.6627\pm0.0002$, where the exact value is $h_2=0.662798972834$. For three-dimensional lattice with periodic condition, our numerical result is $0.7847\pm0.0014$, {which agrees with the best known bound $0.7653 \leq h_3 \leq 0.7862$.}Comment: 6 pages, 2 figure

Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors

In a recent paper [B. A. Piot et al., Phys. Rev. B 72, 245325 (2005)], we have shown that the lifting of the electron spin degeneracy in the integer quantum Hall effect at high filling factors should be interpreted as a magnetic-field-induced Stoner transition. In this work, we extend the analysis to investigate the influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors. The single-particle Zeeman energy is tuned through the application of an additional in-plane magnetic field. Both the evolution of the spin polarization of the system and the critical magnetic field for spin splitting are well described as a function of the tilt angle of the sample in the magnetic field.Comment: Published in Phys. Rev.

Bounds on the Magnetic Fields in the Radiative Zone of the Sun

We discuss bounds on the strength of the magnetic fields that could be buried in the radiative zone of the Sun. The field profiles and decay times are computed for all axisymmetric toroidal Ohmic decay eigenmodes with lifetimes exceeding the age of the Sun. The measurements of the solar oblateness yield a bound <~ 7 MG on the strength of the field. A comparable bound is expected to come from the analysis of the splitting of the solar oscillation frequencies. The theoretical analysis of the double diffusive instability also yields a similar bound. The oblateness measurements at their present level of sensitivity are therefore not expected to measure a toroidal field contribution.Comment: 15 pages, 6 figure

Cobalt-based Nanoreactors in Combined Fischer-Tropsch Synthesis and Hydroprocessing: Effects on Methane and CO2_{2} Selectivity

Fischer-Tropsch synthesis: Four types of bi-functional catalysts with cobalt nanoparticles supported on meso- or microporous silicates or aluminosilicates are investigated regarding the obtained CO$_{2}$ and CH$_{4l}$ selectivity under low-temperature Fischer-Tropsch reaction conditions. In situ x-ray absorption spectroscopy results under industrially relevant conditions reveal that strong cobalt-support interactions and oxidized cobalt species are the main factors determining the selectivity depending on the specific support material used. The production of liquid hydrocarbons from syngas (CO and H$_{2}$) via the combined Fischer-Tropsch (FT) synthesis and hydroprocessing (HP) is a promising strategy to provide valuable chemicals and fuels based on renewable feedstocks. High yields of liquid products are essential for industrial implementation since short-chain side products like methane and CO$_{2}$ reduce the overall carbon efficiency, which holds true especially for bi-functional Co/zeolite catalysts. In order to investigate the influence of the support material properties on the methane and CO$_{2}$ selectivities in the combined FT and HP reaction, we synthesized four well-defined catalyst materials with similar cobalt particle sizes. The active material is supported on either meso- or microporous silicates or aluminosilicates. The catalytic properties are investigated in FT experiments at industrially relevant conditions (20 bar, 200–260 °C) and correlated with in situ x-ray absorption spectroscopy results to determine the chemical environment responsible for the selectivity observed. The origin of the high methane selectivity detected for crystalline and amorphous aluminosilicate was mainly traced back to the strong cobalt-support interactions. The high CO$_{2}$ selectivity, observed only for crystalline zeolite materials, is driven by the presence of oxidized cobalt species, while the acidic support in combination with micropores and possible overcracking leads to the observed drop in the C$_{5+}$ selectivity

The influence of collective neutrino oscillations on a supernova r-process

Recently, it has been demonstrated that neutrinos in a supernova oscillate collectively. This process occurs much deeper than the conventional matter-induced MSW effect and hence may have an impact on nucleosynthesis. In this paper we explore the effects of collective neutrino oscillations on the r-process, using representative late-time neutrino spectra and outflow models. We find that accurate modeling of the collective oscillations is essential for this analysis. As an illustration, the often-used "single-angle" approximation makes grossly inaccurate predictions for the yields in our setup. With the proper multiangle treatment, the effect of the oscillations is found to be less dramatic, but still significant. Since the oscillation patterns are sensitive to the details of the emitted fluxes and the sign of the neutrino mass hierarchy, so are the r-process yields. The magnitude of the effect also depends sensitively on the astrophysical conditions - in particular on the interplay between the time when nuclei begin to exist in significant numbers and the time when the collective oscillation begins. A more definitive understanding of the astrophysical conditions, and accurate modeling of the collective oscillations for those conditions, is necessary.Comment: 27 pages, 10 figure

Sexual Risk Behaviour among HIV-Positive Individuals in Clinical Care in Urban KwaZulu-Natal, South Africa

Objectives: To assess the prevalence and predictors of unprotected sex among HIV+ individuals in clinical care in urban KwaZulu-Natal, South Africa. Design: Cross-sectional survey of 152 HIV+ individuals attending a hospital-based HIV-clinic. Methods: Structured interviews were conducted by bilingual interviewers. Sexual risk behaviour in the preceding 3 months was assessed via event counts. Results: In one of the first studies of its kind in South Africa we found that nearly half of the sample reported vaginal or anal sex during the preceding 3 months, and 30% of these patients reported unprotected vaginal or anal sex. Among sexually active patients, a total of 171 unprotected sex events were reported, 40% of which were with partners perceived to be HIV negative or HIV-status unknown. Nine such partners were potentially exposed to HIV. Alcohol use during sex, being forced to have sex, sex with a perceived HIV+ partner, and sex with a casual partner predicted more unprotected sex, whereas HIV-status disclosure was related to less unprotected sex. Conclusions: HIV+ individuals in clinical care in South Africa may engage in unprotected sex that place others at risk of HIV infection and themselves at risk for infection with STIs. With a national ARV rollout currently underway in South Africa, increasing numbers of HIV+ individuals are entering care. This affords a crucial opportunity to link HIV prevention with HIV care, an approach that aims to reduce transmission risk behaviour among HIV+ individuals and is consistent with international agencies’ current prevention priorities

Lower Bounds for Heights in Relative Galois Extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition