Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Tunneling and transmission resonances of a Dirac particle by a double barrier

We calculate the tunneling process of a Dirac particle across two square barriers separated a distance $d$, as well as the scattering by a double cusp barrier where the centers of the cusps are separated a distance larger than their screening lengths. Using the scattering matrix formalism, we obtain the transmission and reflection amplitudes for the scattering processes of both configurations. We show that, the presence of transmission resonances modifies the Lorentizian shape of the energy resonances and induces the appearance of additional maxima in the transmission coefficient in the range of energies where transmission resonances occur. We calculate the Wigner time-delay and show how their maxima depend on the position of the transmission resonance.Comment: To appear in Physica Script

A review of modelling and optimisation methods applied to railways energy consumption

[EN] Railways are a rather efficient transport mean, and yet there is increasing interest in reducing their energy consumption and making them more sustainable in the current context of climate change. Many studies try to model, analyse and optimise the energy consumed by railways, and there is a wide diversity of methods, techniques and approaches regarding how to formulate and solve this problem. This paper aims to provide insight into this topic by reviewing up to 52 papers related to railways energy consumption. Two main areas are analysed: modelling techniques used to simulate train(s) movement and energy consumption, and optimisation methods used to achieve more efficient train circulations in railway networks. The most used methods in each case are briefly described and the main trends found are analysed. Furthermore, a statistical study has been carried out to recognise relationships between methods and optimisation variables. It was found that deterministic models based on the Davis equation are by far (85% of the papers reviewed) the most common in terms of modelling. As for optimisation, meta-heuristic methods are the preferred choice (57.8%), particularly Genetic Algorithms.Martínez Fernández, P.; Villalba Sanchis, I.; Yepes, V.; Insa Franco, R. (2019). A review of modelling and optimisation methods applied to railways energy consumption. Journal of Cleaner Production. 222:153-162. https://doi.org/10.1016/j.jclepro.2019.03.037S15316222

Influence of Gravity on noncommutative Dirac equation

In this paper, we investigate the influence of gravity and noncommutativity on Dirac equation. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved space-time with an operator which depends on the noncommutative $\theta$-parameter. As an application, we have computed the density number of the created particles in presence of constant strong electric field in an anisotropic Bianchi universe.Comment: 9 pages, correct some miprints, Accepted for publication in journal of Mod. Phys. Letters

Breastfeeding media coverage and beliefs during the COVID-19 pandemic in Mexico: implications for breastfeeding equity

Background: Because breastfeeding offers short- and long- term health benefits to mothers and children, breastfeeding promotion and support is a public health priority. Evidence shows that SARS-CoV-2 is not likely to be transmitted via breastmilk. Moreover, antibodies against SARS-CoV-2 are thought to be contained in breastmilk of mothers with history of COVID-19 infection or vaccination. WHO recommends direct breastfeeding as the preferred infant feeding option during the COVID-19 pandemic, even among women with COVID-19; but conflicting practices have been adopted, which could widen existing inequities in breastfeeding. This study aims to describe how information about breastfeeding was communicated in Mexican media during the pandemic and assess Mexican adults’ beliefs regarding breastfeeding among mothers infected with COVID-19. Methods: We conducted a retrospective content analysis of media coverage on breastfeeding in Mexico between March 1 and September 24, 2020, excluding advertisements. For the content analysis, we performed both a sentiment analysis and an analysis based on strengths, weaknesses, opportunities, and threats (SWOT) for breastfeeding promotion. Additionally, we conducted a descriptive analysis of nationally representative data on adults’ beliefs about breastfeeding from the July 2020 round of the ENCOVID-19 survey in Mexico and stratified the results by gender, age, and socioeconomic status. Results: A total of 1014 publications on breastfeeding were identified on the internet and television and in newspapers and magazines. Most information was published during World Breastfeeding Week, celebrated in August. The sentiment analysis showed that 57.2% of all information was classified as positive. The SWOT analysis indicated that most information focused on current actions, messages, policies, or programs that enable breastfeeding (i.e., strengths) or those not currently in place but that may enable breastfeeding (i.e., opportunities) for breastfeeding promotion. However, ENCOVID-19 survey results showed that 67.3% of adults living in households with children under 3 years of age believe that mothers with COVID-19 should not breastfeed, and 19.8% do not know whether these mothers should breastfeed. These beliefs showed differences both by gender and by socioeconomic status. Conclusions: While the Mexican government endorsed the recommendation on breastfeeding during the COVID-19 pandemic, communication was sporadic, inconstant and unequal across types of media. There was a widespread notion that mothers with COVID-19 should not breastfeed and due to differences on beliefs by socioeconomic status, health inequities could be exacerbated by increasing the risk of poorer breastfeeding practices and preventing vulnerable groups from reaping the short and long-term benefits of breastfeeding

Energy spectrum of the relativistic Dirac-Morse problem

We derive an elegant analytic formula for the energy spectrum of the relativistic Dirac-Morse problem, which has been solved recently. The new formula displays the properties of the spectrum more vividly.Comment: Replaced with a more potrable PDF versio

Exact Solution of Photon Equation in Stationary G\"{o}del-type and G\"{o}del Space-Times

In this work the photon equation (massless Duffin-Kemmer-Petiau equation) is written expilicitly for general type of stationary G\"{o}del space-times and is solved exactly for G\"{o}del-type and G\"{o}del space-times. Harmonic oscillator behaviour of the solutions is discussed and energy spectrum of photon is obtained.Comment: 9 pages,RevTeX, no figure, revised for publicatio

Speeding up Entanglement Degradation

Entanglement between two free bosonic modes can be determined via detection of each mode by different observers and then observing the correlations between their measurements. We show that such entanglement is degraded as a function of time if one observer begins in a state of inertial motion but ends in a state of uniform acceleration while the other remains inertial. At late times we recover previously established results for observers in relative uniform acceleration.Comment: 5 pages, 2 figure

Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra

Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole. The beauty and simplicity of these results has led us to explore the similar problems in Atomic Physics when the nuclei have an added Dirac magnetic monopole. These problems have been explored by others and we sketch the derivations and give details of the predicted spectrum of monopolar hydrogen. Finally we return to gravomagnetic monopoles in general relativity. We explain why NUT space has a non-spherical metric although NUT space itself is the spherical space-time of a mass with a gravomagnetic monopole. We demonstrate that all geodesics in NUT space lie on cones and use this result to study the gravitational lensing by bodies with gravomagnetic monopoles. We remark that just as electromagnetism would have to be extended beyond Maxwell's equations to allow for magnetic monopoles and their currents so general relativity would have to be extended to allow torsion for general distributions of gravomagnetic monopoles and their currents. Of course if monopoles were never discovered then it would be a triumph for both Maxwellian Electromagnetism and General Relativity as they stand!Comment: 39 pages, 9 figures and 2 tables available on request from the author