Thermal entanglement witness for materials with variable local spin lengths

We show that the thermal entanglement in a spin system using only magnetic susceptibility measurements is restricted to the insulator materials. We develop a generalization of the thermal entanglement witness that allows us to get information about the system entanglement with variable local spin lengths that can be used experimentally in conductor or insulator materials. As an application, we study thermal entanglement for the half-filled Hubbard model for linear, square and cubic clusters. We note that it is the itinerancy of electrons that favors the entanglement. Our results suggest a weak dependence between entanglement and external spin freedom degrees.Comment: 4 pages, 3 figure

Preparação de sabão com propriedades fitoterápicas e emolientes a partir do óleo vegetal de cozinha.

Diariamente são descartados litros e litros de óleo doméstico usado, uma parte desse descarte se dá em latas de lixo, rede de esgoto, poucos são aqueles que reservam esse tipo de material para reciclagem, uma parte é por não saber como tratar os resíduos contidos em seu meio. Os projetos de preparação de sabão com propriedades fitoterápicas têm por objetivo dar um destino ao descarte desse óleo residual doméstico, promovendo a interação da comunidade local da região da Vila C a fazer desde a parte do tratamento de resíduo do óleo até a mistura de outros reagentes para a produção de um sabão para o banho de animais domésticos e que possa ser utilizável para limpeza de utensílios domésticos. Para a preparação deste material é considerado o fácil acesso aos reagentes envolvidos como a soda cáustica, a qual ainda é comercialmente vendida em mercearias locais e acesso às plantas medicinais que já tem suas propriedades conhecidas, como no caso a erva baleeira, calêndula, e citronela, também é realizado junto a comunidade, oficinas informando sobre os cuidados em manipular produtos químicos, como agir em caso de acidentes durante o manuseio, a quem é indicado a fazer esse tipo de tratamento e como preparar o produto. Existem análises laboratoriais que são acompanhadas e orientadas, as quais são necessárias para testes em pequena escala antes de cada oficina, essas análises são feitas para poder corrigir o pH do produto e mensurar a quantidade de aditivos na produção do sabão, após essas análises o modelo de produção é replicado em escala maior, já com a certeza dos resultados na qualidade do produto final. Desta forma se faz necessário uma investigação mais detalhada ao produto final, por meio de utilização de equipamentos cromatográficos e espectrofotômetros, como ferramenta na identificação dos compostos e/ou princípios ativos na composição, os quais dão a característica de fitoterápicos e comparar desta forma, com o que já temos em literatura conhecida

Chaos in Anisotropic Pre-Inflationary Universes

We study the dynamics of anisotropic Bianchi type-IX models with matter and cosmological constant. The models can be thought as describing the role of anisotropy in the early stages of inflation. The concurrence of the cosmological constant and anisotropy are sufficient to produce a chaotic dynamics in the gravitational degrees of freedom, connected to the presence of a critical point of saddle-center type in the phase space of the system. The invariant character of chaos is guaranteed by the topology of the cylinders emanating from unstable periodic orbits in the neighborhood of the saddle-center. We discuss a possible mechanism for amplification of specific wavelengths of inhomogeneous fluctuations in the models. A geometrical interpretation is given for Wald's inequality in terms of invariant tori and their destruction by increasing values of the cosmological constant.Comment: 14 pages, figures available under request. submitted to Physical Review

Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.

Germany's 'coronavirus anomaly': Statistical evidence that early mass testing leads to low mortality rates

In this note, we present a statistical analysis of the mortality rates of COVID-19 for several selected European countries. We compare the countries' mortality rates with their respective number of tests as a function of the time since the first death. Our analysis shows that countries that either delayed mass testing, such as Italy, or have not fully adopted it, such as France and the UK, have had much higher mortality rates than Germany, which has adopted a policy of wide and early testing. Conversely, countries that have followed Germany's example, such as Portugal, have so far had comparatively low mortality rates

Chaotic Friedmann-Robertson-Walker Cosmology

We show that the dynamics of a spatially closed Friedmann - Robertson - Walker Universe conformally coupled to a real, free, massive scalar field, is chaotic, for large enough field amplitudes. We do so by proving that this system is integrable under the adiabatic approximation, but that the corresponding KAM tori break up when non adiabatic terms are considered. This finding is confirmed by numerical evaluation of the Lyapunov exponents associated with the system, among other criteria. Chaos sets strong limitations to our ability to predict the value of the field at the Big Crunch, from its given value at the Big Bang. (Figures available on request)Comment: 28 pages, 11 figure