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

Transmission resonances and supercritical states in a one dimensional cusp potential

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.Comment: 10 pages. Revtex 4. To appear in Phys Rev.

Two electron entanglement enhancement by an inelastic scattering process

In order to assess inelastic effects on two fermion entanglement production, we address an exactly solvable two-particle scattering problem where the target is an excitable scatterer. Useful entanglement, as measured by the two particle concurrence, is obtained from post-selection of oppositely scattered particle states. The $S$ matrix formalism is generalized in order to address non-unitary evolution in the propagating channels. We find the striking result that inelasticity can actually increase concurrence as compared to the elastic case by increasing the uncertainty of the single particle subspace. Concurrence zeros are controlled by either single particle resonance energies or total reflection conditions that ascertain precisely one of the electron states. Concurrence minima also occur and are controlled by entangled resonance situations were the electron becomes entangled with the scatterer, and thus does not give up full information of its state. In this model, exciting the scatterer can never fully destroy phase coherence due to an intrinsic limit to the probability of inelastic events.Comment: 8 pages, to appear in Phys. Rev

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

Regional Differences in South American Monsoon Precipitation Inferred from the Growth and Isotopic Composition of Tropical Trees

The authors present results on the relationship between tree-ring proxies and regional precipitation for several sites in tropical South America. The responsiveness of oxygen isotopes (δ18O) and seasonal growth as precipitation proxies was first validated by high-resolution sampling of a Tachigali myrmecophila from Manaus, Brazil (3.1°S, 60.0°W). Monthly growth of Tachigali spp. was significantly correlated with monthly precipitation. Intra-annual measurements of cellulose δ18O in Tachigali spp. were also significantly correlated with monthly precipitation at a lag of approximately one month. The annual ring widths of two tropical tree taxa, Cedrela odorata growing in the Amazon (12.6°S, 69.2°W) and Polylepis tarapacana growing in the Altiplano (22.0°S, 66.0°W), were validated using bomb-derived radiocarbon 14C. Estimated dates were within two to three years of bomb-inferred 14C dates, indicating that these species exhibit annual rings but uncertainties in our chronologies remain. A multiproxy record spanning 180 years from Cedrela spp. showed a significant negative relationship between cellulose δ18O and January precipitation. A 150-yr record obtained from Polylepis spp. also showed a significant negative relationship between δ18O and March precipitation, whereas annual ring width showed a significant positive correlation with December precipitation. These proxies were combined in a multivariate framework to reconstruct past precipitation, revealing a significant increase in monsoon precipitation at the Amazon site since 1890 and a significant decrease in monsoon precipitation at the Altiplano since 1880. Proxy time series also showed spatial and temporal coherence with precipitation variability due to El Niño forcing, suggesting that oxygen isotopes and ring widths in tropical trees may be important diagnostics for identifying regional differences in the response of the tropical hydrologic cycle to anthropogenic warming

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