Vol. 67 No. 2 Mar-Apr (2021): Revista Mexicana de Física

This Letter reports the breaking of the spherical symmetry in the complete electromagnetic multipole expansion when its sources are distributed on spherical toroidal surfaces, identifying the specic geometrical and physical changes from
the familiar case of sources on a spherical surface. In fact, for spherical toroids dened by concentric spherical rings and symmetric conical rings, the boundary conditions at the latter are not compatible in general with integer values for the orbital angular momentum label of the multipole moments: the polar angle eigenfunctions become Legendre functions of order λ and associativity m represented as innite series with a denite parity, and their complementary associated radial functions are spherical Bessel functions of the same order λ. Consequently, the corresponding multipole sources for the electric, magnetic and toroidal moments and their connections are identied within the Debye formalism, and the
appropriate outgoing wave Green functions are constructed in the new basis of eigenfunctions of the Helmholtz equation. Our familiarity with the exact solutions, for the cases of the complete sphere and of cylindrical toroids, allow us to give a preliminary account of the electromagnetic elds for the spherical toroids via the integration of their sources and the Green function for resonant cavities and optimum effciency antennas.

We show that the technique of Stark-chirped rapid adiabatic passage (SCRAP), can be implemented in tripod quantum systems. We propose a scheme for coherent superposition among two ground states via Stark-shiftchirped rapid adiabatic passage technique in a tripod system. Tripod-SCRAP uses four laser pulses: an intense far-off-resonance Stark laser pulse modifies the transition frequency between the states by Stark shifting their energies and three nearly resonant pump, Stokes, and control laser pulses that fractionally transfer the population between the ground states via adiabatic passage. In our scheme, the pulse duration of the pump pulse must be larger than the pulse duration of the Stokes and control pulses, although with a smaller amplitude, and the atom encounters with the pump, Stokes, control, and Stark laser pulses with counterintuitive order (Stokes pulse arrives before the rest of the pulses). This technique can be applied to one-photon as well as multiphoton transitions and it is not necessary to vanish the pulses (pump and Stokes) simultaneously and it is a powerful alternative tool for f-STIRAP and tripod-STIRAP techniques at least when inhomogeneous broadenings are included. inhomogeneous broadening. This technique is robust against moderate variations in the intensities of the laser pulses,in detunings, and in delays between the pulses.

Experiments on electronic excitation of molecules using positron as incident particle have shown much larger cross sections than in the electron scattering case.  The comprehension of these inelastic processes represent a great challenge and only few studies on electronic excitation of molecules are discussed in the literature. For example, for the C₆H₆ molecule experimental and theoretical calculations are not in a very advanced state same for electron scattering case (Benzene represent a simplest aromatic hydrocarbon and very important chemical compound due to its role as a key precursor in process pharmaceutical). Recent experiments on electronic excitation of C₆H₆ (¹B_1u, and ¹E_1u electronic states) using electron as incident particle are available by Kato et al (J.Chem.Phys.134 134308(2011)). Motivated by their experiments we have taken up the task to investigate the same electronic excitation of C₆H₆ using positron as incident particle.  For the first time, integral cross sections in e⁺ - C₆H₆ (¹B_1u, and ¹E_1u electronic states) using the scaling Born positron (SBP) approach are reported and in the absence of the experimental data and developments theoretical, comparisons are made with analogous electron scattering.

Keywords: Born, positron, scaling

Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

Ground state and 1st excited state energies and wave functions were calculated for systems of one or two electrons in a 2D and 3D potential well having a shape intermediate between a circle and a square or a sphere and a cube. One way to define such a potential well is with a step potential and a bounding surface of form $|x|^q+|y|^q+|z|^q = |r|^q$, which converts from a sphere to a cube when $q$ increases from $2$ to infinity. This kind of geometrical object is called a Lam\'{e} surface. The calculations were done either with implicit finite difference time stepping in the direction of negative imaginary time axis or with quantum diffusion Monte Carlo. The results demonstrate how the volume and depth of the potential well affect the $E_0$ more than the shape parameter $q$ does. Functions of two and three parameters were found to be sufficient for fitting an empirical graph to the ground state energy data points as a function of well depth $V_0$ or exponent $q$. The ground state and first excited state energy of one particle in a potential well of this type appeared to be very closely approximated with an exponential function depending on $q$, when the well depth and area or volume was kept constant while changing the value of $q$. The model is potentially useful for describing quantum dots that deviate from simple geometric shapes, or for demonstrating methods of computational quantum mechanics to undergraduate students.

We study the mechanism of particle creation in the context of the emergent universe (EU) scenario which is privileged by certain important characteristics such as the absence of time-like singularity. EU asymptotically coincides with an Einstein static model in the infinite past and it approaches to a de Sitter expansion phase at late times. By introducing the conformal time, we obtain the solution of the Klein-Gordon equation and by applying the "in" and "out" states method, the total number of produced particles and the total energy associated with them are determined.

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator is investigated and illustrates the wave functions in the momentum space. The eigensolutions are found and the system is mapping to the well-known Schrodinger equation in a Pöschl-Teller potential.

We report a Costas loop for demodulation of an optical field with binary phase modulation (BPSK). The loop operates in the domain of digital signal processing (DSP) as part of an intradyne coherent digital receiver. The practical implementation of BPSK demodulation in the optical domain is generally not feasible. For this reason, we use techniques based on high-speed digitization of the post-photodetection electrical observable, and the Costas loop in DSP acts on the digitized signal. We chose this loop because it is an optimal structure for both BPSK demodulation and carrier synchronization. Typically, Costas loops for BPSK demodulation operate on a carrier with a frequency higher than the bit rate. However, as we demonstrate in this work, this loop can also perform adequately for a bit rate higher than the carrier frequency (intradyne detection). To the best of our knowledge, the Costas loop in DSP for intradyne BPSK demodulation is reported for the first time in this work. To design the intradyne Costas loop, we used the PLL-equivalent model of a conventional Costas loop. For comparison and performance evaluation, we implemented in simulation, first, a traditional Costas loop and later an intradyne one. We use real-world signals (binary data and additive noise) acquired by digitization for our simulations. Finally, we performed the intradyne Costas loop’s characterization using a digitized post-photodetection electrical signal obtained at the output of our digital coherent receiver. We observe a performance very close to that obtained by simulation.

In the present paper we report a novel synthesis method of silicon quantum dots (SiQDs) using 3-Aminopropyltriethoxysilane (APTES) as silicon precursor and low molecular weight chitosan (CS) as reducing agent. The obtained SiQDs have a hydrodynamic diameter of 2.3 nm, water dispersible, presents blue emission band at 434.5 nm (2.85 eV) with a Commission Internationale de l’Eclairage 1931 (CIE1931) chromaticity coordinates (x = 0.1665, y = 0.1222), the experimental absorbance of the SiQDS was measured and the band gap (Eg) was estimated through PerkinElmer’s method, the obtained value was 3.1 eV and a positive ζ-potential of + 35 mV, resulting in photonics, microelectronics, and biotechnological potential applications.

Structural and thermoelectric properties of rare-earth zirconates A₂Zr₂O₇, with A = Pr, Nd, Sm, Gd, and Er, were studied. Samples were prepared by solid-state reaction at ambient pressure with temperatures between 1000 and 1400 °C. The resulting compounds were characterized by X-ray diffraction (XRD) and scanning electron microscopy (SEM/EDS). The XRD analyses showed the formation of polycrystalline Pr₂Zr₂O₇, Nd₂Zr₂O₇, Sm₂Zr₂O₇, Gd₂Zr₂O₇ and Er₂Zr₂O₇ phases, with a cubic cell (space group Fm3m) and traces of the raw used materials. The micrographs obtained by SEM show the formation of heterogeneous grains with a size that ranges from 0.7 to 4.7 μm. All A₂Zr₂O₇ samples present porous surfaces. Thermal conductivities were measured at different temperatures, from 300 to 900 K. In most of the samples, the thermal conductivity monotonically decreases with temperature, from 0.40 – 1.17 W/mK at 300 K to 0.27 – 0.77 W/mK at 773.15 K. At a fixed temperature, the thermal conductivity decreases almost monotonically with the ionic radius (IR) of the rare-earth elements (where IR (Er³⁺) = 0.890 Å < IR (Gd³⁺) = 0.938 Å < IR (Sm³⁺) = 0.958 Å < IR (Nd³⁺) = 0.983 Å < IR (Pr³⁺) = 0.99 Å).

This study is focused on the investigation of SnS thin film for transistor application. Electron trap which is associated with grain boundary effect affects the electrical conductivity of SnS semiconductor thin film thereby militating the attainment of the threshold voltage required for transistor operation. Grain size and grain boundary is a function of a semiconductor’s thickness. SnS semiconductor thin films of 0.20, 0.25, 0.30, 0.35, 0.40 μm were deposited using aerosol assisted chemical vapour deposition on glass substrates. Profilometry, Scanning electron microscope, Energy dispersive X-ray spectroscopy and hall measurement were used to characterise the composition, microstructure and electrical properties of the SnS thin film.  SnS thin films were found to consist of Sn and S elements whose composition varied with increase in thickness. The film conductivity was found to vary with grain size and grain boundary which is a function of the film thickness. The SnS film of 0.4 μm thickness shows optimal grain growth with a grain size of 130.31 nm signifying an optimum for the as deposited SnS films as the larger grains reduces the number of grain boundaries and charge trap density which allows charge carriers to move freely in the lattice thereby causing a reduction in resistivity and increase in conductivity of the films which is essential in obtaining the threshold voltage for a transistor semiconductor channel layer operation. The carrier concentration of due to low resistivity of 3.612 ×10⁵ Ωcm of 0.4 μm SnS thin film thickness is optimum and favours the attainment of the threshold voltage for a field effect transistor operation hence the application of SnS thin film as a semiconductor channel layer in a field effect transistor.

This study investigates metallic inclusions in ground maize forms of dry, paste and wet using domestic grinding machine and its health implications to human. With progressive maize processing using the grinding machine, metals are introduced as contaminants into ground maize due to wear and tear of the grinding discs and other machine parts. Maize samples of 1 kg each were grinded in wet, paste, and dry forms. The metallic inclusions were extracted from the ground maize forms using magnetisation, sedimentation and decantation. The extractions were quantified using an Electronic weighing balance and were characterised using, Scanning Electron Microscopy, Optical Emission Microscopy and Energy Dispersive Spectroscopy. Iron fillings were discovered to be the dominant metallic inclusion present in the various food forms and also in the grinding disc with 88.48% by weight in the grinding disc. The extracted metallic inclusions is 0.157g/kg, 0.196g/kg and 0.268 g/kg for dry, paste and wet ground maize forms which exceeded the World Health Organisation limit of 15 mg/kg. The EDS result show that the wet form has the highest amount of metallic inclusions of 95.97 at. %, the paste form with 91.39 at. % and dry form with 83.35 at. %. From the SEM analysis of particle size, the dry, paste and wet ground maize had 17μm, 27μm and 36μm particle sizes respectively. When in excess the Iron filling metallic inclusions from the ground maize accumulates in body organs since there is no physiological mechanism to eliminate excess iron thereby leading to health complications. The accumulated iron in the heart causes increased risk of cardiovascular diseases, siderosis and hemochromatosis in the liver leading to hepatoma-the primary cause of cancer of the liver among others. Elevated levels of free iron also predisposed individuals to high risk of bacterial and viral infections leading to death.

Available experimental angular distribution data for ⁶Li+²⁸Si elastic scattering in the energy range 16 – 318 MeV are re-analyzed phenomenologically on the basis of optical model using Woods-Saxon (WS) potentials for both real and imaginary parts, while the semi microscopic analysis was performed on the basis of cluster folding potential. Cluster folding potential was generated based on the appreciable cluster structure and breakup of ⁶Li into a deuteron orbiting a core of α-particle. Although several data sets in a wide range of energies are subjected to investigation, the theoretical calculations using the different concerned potentials are fairly reproduced the experimental data in the whole energy range. The extracted real and imaginary volume integrals and reaction cross sections values are compared to the previously reported ones and they found to be in a good agreement

We investigate the structure of the  optical field radiated by the disordered optical nano-emitters randomly incorporated  in three-dimensional cluster of a percolation material. Our numerical studies shown that the temporal variations of the inverse participation ratio (IPR) allow analyzing the extended and localized field structures over a long time range. The properties of IPR and the dynamics of the lasing emitters allow to find the characteristic time scales when the localization of the field in a general three-dimensional disordered system occurs. The studied effect opens new perspectives to control the optical fields localization in modern optical nano-technologies.

Photon Scattering Profiles in a turbid media were investigated through numerical simulation based on Monte Carlo-Mie method, at this present work. Using Wolfram Mathematics in the program algorithm. Photon Scattering was treated using electromagnetic spherical harmonics waves, in three-dimensional scattering. The proposal, as an alternative to the Henyey-Greensein phase approximation, was defining an unit vector that represents a phase distribution, as an equivalent function with three vector components, within the turbid media. Associating the step component, as projection using Legendre polynomials and for the transverse plane components were defining as vector bases in terms of Legendre-Hankel functions, according to Gustav Mie theory. This composite vector was defined as a step function and was evaluated within Monte Carlo algorithm, obtaining simulations of light scattering. Backscatter profiles were compared for different geometric dimensions of the spherical particles within the turbid media, including a validation of the model with an experimental Lidar signal from low clouds, obtaining physical properties of the turbid media by the proposed theoretical model.

In this theoretical study, we presents  for the first time, to the best of our knowledge, the structural, electronic and elastic properties of perovskite Sr_0.5Be_0.5TiO₃ type structure (Tetragonal), P4/mmm, space group, 123.using full potential linearized augmented plane wave (FP-LAPW) method on the basis of density functional theory (DFT) integrated in the Wien2k code . The generalized gradient approximation (GGA-PBEsol) and local density approximation has been used for the exchange correlation potential .The electronic properties represented by the band structure (BS) and DOS as well as the (PDOS) partial density of states, allowed to obtain  semiconductor compound, which have been calculated with mBJ approximation. The elastic constants were reported and we verified the stability conditions of our materials elastically. These theoretical results open the way for experimental and other theoretical studies of this compound.

The crystal structure of the new CuFeInTe₃ quaternary compound was studied by the Rietveld method from powder X-ray diffraction data. The CuFeInTe₃ compound crystallize in the tetragonal CuFeInSe₃-type structure with space group P2c (Nº 112), and unit cell parameters a = 6.1842(1) Å, c = 12.4163(2) Å, V = 474.85(1) ų. The density of CuFeInTe₃ is rx = 5.753 g cm⁻³. The reliability factors of the Rietveld refinement results are R_p= 5.5%, R_wp= 6.1%, R_exp= 4.7%, and S= 1.3. The powder XRD data of CuFeInTe₃ are presented and the figures of merit of indexation are M₂₀ = 79.4 and F₃₀ = 43.3 (0.0045, 154).

In a previous work reported in this journal, the thermodynamical properties of d-wave superconducting ground states close to half filling
were obtained by using a generalized Hubbard model.

Aluminum nitride is attracting great interest of the industry and scientific community due to its interesting properties. In this paper is performed a theoretical study on the ultrafast transient transport properties of photoinjected carriers in wurtzite AlN subjected to electric fields up to 80 kV/cm. For this, the Nonequilibrium Statistical Operator Method was used. The evolution towards the steady state of drift velocity of carriers (electrons and holes) and nonequilibrium temperature (carriers and phonons) subpicosecond scale were determined.

In the study of problems related to epilepsy analyzing electroencephalograms data is of much importance to help, one hand, to its diagnosis, and, another hand in the possibility of diminishing errors in surgery. We do this analysis making the Feigenbaum graphs for real electroencephalographic signals data sets and calculating characteristic networks (graph) quantities, such as average clustering, degree distribution, and average shortest path length. 
We manage to characterize two different data sets from each other, from data sets corresponding to focal and non-focal neuronal activity both time out of an epileptic seizure. This method enables us to identify sets of data from epileptic focal zones and suggest our approach could be used to aid physicians with diagnosing epilepsy from electroencephalographic data and/or in an exact establishment of the epileptic focal region for surgery.

A different manner of study synchronization between chaotic systems is presented. This is done by using two different forced coupled nonlinear circuits. The way of coupling the systems under study is different from those used in the analysis of chaos in dynamical systems of low dimensionality. The study of synchronization and how to manipulate it, is carried out through the variation of the couplings by calculating the bifurcation diagrams. We observed that for rather larger values of the coupling between the circuits it is reached total synchronization, while for small values of the coupling it is obtained, in the best of the cases, partial synchronization.