Evolution of quantum observables: from non-commutativity to commutativity

A fundamental aspect of the quantum-to-classical limit is the transition from a non- commutative algebra of observables to commutative one.However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infinite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.MINECO Grant MTM2014- 57129-C2-1-P. Junta de Castilla y Leon Grants BU229P18, VA137G18

Newtonian Flow in Converging-Diverging Capillaries

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.Comment: 23 pages, 5 figures, 1 table. This is an extended and improved version. arXiv admin note: substantial text overlap with arXiv:1006.151

The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity

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Spectral properties of the two-dimensional Schrödinger Hamiltonian with various solvable confinements in the presence of a central point perturbation

We study three solvable two-dimensional systems perturbed by a point interaction centered at the origin. The unperturbed systems are the isotropic harmonic oscillator, a square pyramidal potential and a combination thereof. We study the spectrum of the perturbed systems. We show that, while most eigenvalues are not affected by the point perturbation, a few of them are strongly perturbed. We show that for some values of one parameter, these perturbed eigenvalues may take lower values than the immediately lower eigenvalue, so that level crossings occur. These level crossings are studied in some detail

Uso de los foros de discusión en un programa de enseñanza destinado a adultos

Hacer más factibles, reales y duraderos los procesos de aprendizaje para la población adulta trabajadora y públicos en general, teniendo en cuenta la importancia creciente de la formación profesional en ambientes altamente exigentes y dinámicos, constituye en la actualidad un imperativo impostergable para todos los profesionales de una u otra especialidad relacionados con la tarea de enseñar y que exige, además de manejar profundamente las características psicológicas de la etapa de desarrollo evolutiva de que se trate en función de potenciar el desarrollo de todos, el dominio o preparación del docente en las novedosas tecnologías de la información así como su implementación exitosa en pos de un aprendizaje no sólo eficaz, sino también colaborativo, donde se aprovechen e intervengan las fuerzas de todos los miembros del grupo. Por las razones expuestas anteriormente implementamos el uso de una plataforma interactiva para el desarrollo de un curso dirigido a los docentes de nuestro centro denominado Aprendizaje en adultos estructurado en 5 temas que se presentan al estudiante mediante guías de estudio, incluyendo también un ejercicio de evaluación final, y que presenta determinadas particularidades partiendo de nuestras condiciones concretas, las cuáles se expresan de manera amplia en el artículo presentado

Connection between inelastic x-ray scattering and complementary x-ray spectroscopies: probing excitons at Al K and L1 edges of α\alpha-Al2_2O3_3

We present an ab initio study of core excitations at the aluminum K and L1 edges in ${\alpha}$-Al2O3 within an all-electron many-body perturbation theory (MBPT) framework. Calculated XAS reveals excellent agreement with experiments, highlighting the dipole-forbidden nature of the pre-peak, which in experiments is enabled by sp mixing due to atomic vibrations. Non-resonant inelastic X-ray scattering (NRIXS) is employed to go beyond the dipole approximation and probe transition channels with s, p, and d character, enhancing multipole transitions that contribute to the pre-peak. The RIXS spectra at K and L1 edges are remarkably similar, opening the way to soft X-ray RIXS experiments to probe semi-core s states. The RIXS calculations reveal two distinct regimes based on the behavior with incoming photon energy ($\omega_1$). For $\omega_1$ in resonance with the XAS threshold, we observe Raman-like behavior, where the RIXS spectra show significant dependence on $\omega_1$ , reflecting the coupling between absorption and emission processes. For higher $\omega_1$ , above the XAS threshold, the study reveals fluorescence features that appear at constant emission energy, and can be explained via X-ray emission spectroscopy (XES)

Solutions to muscle fiber equations and their long time behaviour

We consider the nonlinear initial-boundary value problem governing the dynamical displacements of a one dimensional solid body with specific stress-strain law. This constitutive law results from the modelization of the mechanisms that rules the electrically activated mechanical behaviour of cardiac muscle fibers at the microscopic level. We prove global existence and uniqueness of solutions and we study their asymptotic behaviour in time. In particular we show that under vanishing external forcing solutions asymptotically converge to an equilibrium

Prediction of weld line location for injection molded thermoplastic components

Weld lines in polymeric injection molded parts occur wherever two or more melt fronts meet. They cause reduced mechanical properties and visual defects due to the poor intermolecular entanglement, molecular orientation induced by the fountain flow and the stress concentration effect of surface V-notch. A challenge related to these defects is that they are hard to detect and monitor because they’re usually not visible to the naked eye. Through this paper a numerical model for mold filling simulations has been developed aiming to predict the location of this defect and the initial meeting angle between the colliding flow fronts. A hybrid interface tracking technique was implemented in conjunction with a fix topology pseudo-quadratic mesh. Navier-Stokes equations were reduced to Hele-Shaw equations for thin plates. For validating purposes polypropylene plates injection moldings with weld lines were produced using a two-gated mold in a laboratory scale injector machine. Location of the defect was measure using an optical polariscope and then contrasted with simulation results. In order to establish the differences between 3D and Hele-Shaw models, predictions of weld line location were compared with the results provided by commercial injection molding simulation package Moldex3D.Publicado en: Mecánica Computacional vol. XXXV, no. 6Facultad de Ingenierí