Scielo RSS <![CDATA[Revista mexicana de física]]> vol. 61 num. 3 lang. es <![CDATA[SciELO Logo]]> <![CDATA[<b>The random walk of an electrostatic field using parallel infinite charged planes</b>]]> We show that it is possible to generate a random walk with an electrostatic field by means of several parallel infinite charged planes in which the surface charge distribution could be either ±ó. We formulate the problem of this stochastic process by using a rate equation for the most probable value for the electrostatic field subject to the appropriate transition probabilities according to the electrostatic boundary conditions. Our model gives rise to a stochastic law when the charge distribution is not deterministic. The probability distribution of the electrostatic field intensity, the mean value of the electrostatic force and the energy density are obtained. <![CDATA[<b>Laser scribing of fluorine doped tin oxide for serial interconnection of CdS/CdTe solar cells</b>]]> In thin film PV-module production the scribing of transparent conducting oxides, like fluorine doped tin oxides thin films, is performed with serial interconnection of solar cells without the use of external wires. This scribing is usually carried out with infrared and ultraviolet lasers, while for the other films that complete the solar cell structure, the scribing is performed with visible laser light. Thus, the use of only one laser in all scribing steps in the monolithic interconnection process could reduce the manufacture cost of PV-CdTe modules. In this work the laser scribing process on fluorine doped tin oxides is investigated using a Nd:YAG pulsed laser of 532 nm of wavelength with pulse duration of 50 nanoseconds. The corresponding threshold fluence was measured and the mechanism of interaction of laser radiation with the semiconductor oxide was studied, as well as the temperature distribution along the film and the time when it reached its maximum value after applying the pulse of radiation on the SnO2 :F layer. <![CDATA[<b>Synthesis and magnetic characterization of LaMnO<sub>3</sub> nanoparticles</b>]]> LaMnO3 Nanoparticles systems were prepared by the sol-gel auto-combustion method, in order to analyze the structure and magnetic behavior presented by the compound prepared following a new alternative route of synthesis. Structural characterization, morphology and crystallite size was performed by X-ray diffraction (XRD), infrared spectroscopy (IR) and electron microscopy (TEM). The XRD study together with a Rietveld analysis showed that the LaMnO3 compound crystallized in a perovskite hexagonal structure. The IR spectra showed that the compound has tensile energy bands in the Mn-O-Mn bonds related with the octahedron MnO6; which are attributed to a characteristic vibration of the ABO3 perovskite. An estimated size and morphological analysis was carried out by applying the Scherrer's formula and using Transmission Electron Microscopy (TEM), revealing non-spherical shape and particle sizes between 13 nm and 18 nm. The magnetic measurements M(T) were performed by using zero-field-cooled (ZFC) and field-cooled (FC) protocols which revealed a positive Weiss temperature indicating the presence of ferromagnetic interactions with a Curie temperature, T C = 150 K. <![CDATA[<b>Discrete symmetry in graphene</b>: <b>the Dirac equation and beyond</b>]]> In this paper we review the discrete symmetries of the Dirac equation using elementary tools, but in a comparative order: the usual 3 + 1 dimensional case and the 2 + 1 dimensional case. Motivated by new applications of the 2d Dirac equation in condensed matter (e.g. graphene), we further analyze the discrete symmetries of a full tight-binding model in hexagonal lattices without conical approximations. We touch upon an effective CPT symmetry breaking that occurs when deformations and second-neighbor corrections are considered.<hr/>En este artículo revisamos las simetrías discretas de la ecuación de Dirac usando herramientas fundamentales, en un orden comparativo: el caso commi 3 + 1 dimensional y el caso reducido 2 + 1 dimensional. Motivados por nuevas aplicaciones de la ecuación de Dirac 2d en materia condensada (v. gr. grafeno), también analizamos las simetrías discretas de un modelo de amarre fuerte en redes hexagonales más allá de las aproximaciones cónicas. Hacemos breve mención de un rompimiento de simetría CPT efectiva que ocurre cuando se consideran deformaciones de la red e interacciones a segundos vecinos. <![CDATA[<b>Tunneling of polymer particles</b>]]> In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer tunneling time converge to its quantum-mechanical counterparts in a clear fashion. As the energy approaches the maximum these polymer quantities abruptly decrease to zero. We use the transfer matrix method to study the tunneling through a series of identical potential barriers. We obtain that the transmission coefficients (polymer and quantum-mechanical) behave qualitatively in a similar manner, as expected. Finally we show that the polymer tunneling time exhibits anomalous peaks compared with the standard result. Numerical results are also presented. <![CDATA[<b>Hamiltonian dynamics for Proca's theories in five dimensions with a compact dimension</b>]]> The canonical analysis of Proca's theory in five dimensions with a compact dimension is performed. From the Proca five dimensional action, we perform the compactification process on a S¹/Z2 orbifold, then, we analyze the four dimensional effective action that emerges from the compactification process. We report the extended action, the extended Hamiltonian and we carry out the counting of physical degrees of freedom of the theory. We show that the theory with the compact dimension continues laking of first class constraints. In fact, the final theory is not a gauge theory and describes the propagation of a massive vector field plus a tower of massive KK-excitations and one massive scalar field. Finally, we develop the analysis of a 5D BF-like theory with a Proca mass term, we perform the compactification process on a S¹/Z2 orbifold and we find all the constraints of the effective theory, we also carry out the counting of physical degrees of freedom; with these results, we show that the theory is not topological but reducible in the first class constraints. <![CDATA[<b>Complete sets of circular, elliptic and bipolar harmonic vortices on a plane</b>]]> A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as the curl of a vector potential, which will then satisfy Poisson's equation with vorticity as a source term. In regions with zero vorticity, Poisson's equation reduces to Laplace's equation, and this allows for the construction of harmonic potentials inside and outside circles and ellipses, depending on the coordinate system. The vector potential is normal to the coordinate plane, and is proportional to the scalar harmonic functions on the plane, thereby guaranteeing that the velocity field is also harmonic and is located on the coordinate plane. The components of the velocity field normal to either a circle or an ellipse are continuous, but the tangential components are discontinuous, so that, in effect, a vortex sheet is introduced at these boundaries. This discontinuity is a measure of the vorticity, normal to the plane and distributed harmonically along the perimeter of the respective circles or ellipses. An analytic expression for the streamlines is obtained which makes visualisation of vortices of various geometries and harmonicities possible. This approach also permits a reformulation of the notion of multipolarity of vortices in the traditional sense of a multipolar expansion of the Green function for Poisson's equation. As an example of the applicability of this formulation to known vortical structures, Rankine vortices of different geometries are expressed in terms of harmonic functions. <![CDATA[<b>The Hagen-Beverloo law for outflow of granular solids from holes on side walls</b>]]> In this work we have analyzed experimentally the lateral mass outflow rate m, for cohesionless granular solids (coarse grains) through circular orifices of diameter D made on side walls of bins. Experiments were performed to determine the influence of the wall thickness of the bin w, and of the grain diameter d on m. Geometrical and physical arguments are given to get a general correlation for m as a function of D, d, and w. This correlation can be termed the Hagen-Beverloo law for orifices on side walls.<hr/>En este trabajo analizamos experimentalmente el flujo másico de salida lateral m para sólidos granulares sin cohesión (granos gruesos) a través de orificios circulares de diámetro D realizados sobre las paredes laterales de los recipientes. Se realizaron experimentos para determinar la influencia del grosor de la pared del recipiente, w, y del diámetro de grano, d, sobre m. Se presentan argumentos geométricos y físicos para obtener una correlación general para m como una función de D, d y w. Tal correlación puede ser llamada la ley de Hagen-Beverloo para orificios laterales. <![CDATA[<b>Geometry of spin ½ particles</b>]]> The geometric algebras of space and spacetime are derived by sucessively extending the real number system to include new mutually anticommuting square roots of ±1. The quantum mechanics of spin 1/2 particles are then expressed in these geometric algebras. Classical 2 and 4 component spinors are represented by geometric numbers which have parity, providing new insight into the familiar bra-ket formalism of Dirac. The classical Dirac Equation is shown to be equivalent to the Dirac-Hestenes equation, so long as the issue of parity is not taken into consideration, the latter quantity being constructed in such a way that it is parity invarient. <![CDATA[<b>Plataforma de simulación para lazos de sincronización optoelectrónicos con fase continua y conmutada en comunicaciones ópticas coherentes con difusión de fase óptica</b>]]> En este trabajo se presentan los principios de los lazos optoelectrónicos básicos para sincronización de fase óptica en comunicaciones coherentes (ópticas clásicas, así como su aplicación a sistemas de comunicaciones cuánticas empleando estados coherentes débiles (WCS). Se abordan dos lazos de fase continua, el OPLL y el lazo de Costas convencional (LCC) además del lazo de Costas con cuadraturas conmutadas (LCCC), mostrando ventajas y compromisos en su diseño. Con el fin de evaluar el desempeño de estos lazos desarrollamos una plataforma de simulación basándonos en el programa VPI Photonics Maker empleando para esto parámetros de componentes comerciales. Así, mediante el uso de la plataforma desarrollada es posible mostrar la equivalencia en desempeño del LCCC con respecto al LCC y que el LCCC puede tener mejor desempeño que el LCC (si es diseñado adecuadamente) en la etapa de recepción de un sistema de comunicaciones cuánticas coherentes empleando WCS con difusión de fase óptica. Dado que las simulaciones se realizaron basándonos en componentes comerciales, es de esperarse que en la implementación práctica se obtengan resultados experimentales semejantes a los de la plataforma de simulación.<hr/>On this work we present the basic principles of the optoelectronic loops used for optical phase synchronization in classical optical coherent communications as well as their application to quantum communications systems using weak coherent states (WCS). Two loops of continuous phase, the OPLL and the conventional Costas loop (CCL) as well as the Costas loop with switched quadrature (SQCL) are addressed showing their advantages and their implementation trade-offs. In order to evaluate the performance of these loops a simulation platform is developed based on the VPI Photonics Maker software using parameters of commercial components. Thus, by using the platform developed it may be shown the equivalency in the performance of the SQCL with respect to the CCL and that the SQCL may have a better performance than the CCL (if designed properly) in the receiving stage of a quantum communications system that uses WCS with optical phase diffusion. Since the simulations were performed based on parameters of commercial components, it is expected that a practical implementation will obtain very similar results to those of the simulation platform.