Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

Characterizations of Lojasiewicz inequalities and applications

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative characterizations of this type of inequalities for nonsmooth lower semicontinuous functions defined on a metric or a real Hilbert space. In a metric context, we show that a generalized form of the Lojasiewicz inequality (hereby called the Kurdyka- Lojasiewicz inequality) relates to metric regularity and to the Lipschitz continuity of the sublevel mapping, yielding applications to discrete methods (strong convergence of the proximal algorithm). In a Hilbert setting we further establish that asymptotic properties of the semiflow generated by -∂f are strongly linked to this inequality. This is done by introducing the notion of a piecewise subgradient curve: such curves have uniformly bounded lengths if and only if the Kurdyka- Lojasiewicz inequality is satisfied. Further characterizations in terms of talweg lines -a concept linked to the location of the less steepest points at the level sets of f- and integrability conditions are given. In the convex case these results are significantly reinforced, allowing in particular to establish the asymptotic equivalence of discrete gradient methods and continuous gradient curves. On the other hand, a counterexample of a convex C2 function in R2 is constructed to illustrate the fact that, contrary to our intuition, and unless a specific growth condition is satisfied, convex functions may fail to fulfill the Kurdyka- Lojasiewicz inequality.

Precision laser spectroscopy of the ground state hyperfine splitting of hydrogenlike ^209 Bi^82+

The first direct observation of a hyperfine splitting in the optical regime is reported. The wavelength of the M1 transition between the F = 4 and F = 5 hyperfine levels of the ground state of hydrogenlike ^209 Bi^82+ was measured to be \lamda_0 = 243.87(4) nm by detection of laser induced fluorescence at the heavy-ion storage ring ESR at GSI. In addition, the lifetime of the laser excited F = 5 sublevel was determined to be \tau_0 = 0.351(16) ms. The method can be applied to a number of other nuclei and should allow a novel test of QED corrections in the previously unexplored combination of strong magnetic and electric fields in highly charged ions.

Análise sobre diferentes abordagens de configuração eletrônica de elementos apresentados em livros de química

This study aimed to identify and review of the conceptual differences presented by authors of books, focusing on the theme of electronic configuration. It shows the changing concepts of electronic configuration, its implications for the cognitive development of students and their relations with the contemporary world. We identified possible obstacles in books generated in the search for simplifications, situations of different concepts of energy in the electron configuration for sublevels. For this analysis was carried out in several books, and some other general chemistry and inorganic chemistry without distinguishing between level of education, whether secondary or higher. It was found that some books for school books corroborated with higher education, others do not. To check the consistency of what was discussed, it was a survey of 30 teachers, it was found divergent points of responses, particularly with respect to the energy sublevels and authorship of the diagram which facilitated the electron configuration. It was found that the total 22professores, ie, 73,33% answered correctly on the energy sublevel more calcium (Ca) and 80%, ie, 24 teachers responded incorrectly on the iron. As for the authorship of the diagram used to facilitate the electronic configuration, we obtained 93, 33% of teachers indicated that they followed a diagram, and this was called "Diagram of Linus Pauling," teacher 01, 3,33%, indicated that the diagram was authored by Madelung and 01, 3,33%, did not respond to question. Was observed that it is necessary a more detailed assessment of ancient writings, as the search for simplifications and generalizations, not so plausible, lead to errors and consequences negative for understanding the properties of many substances. It was found that quantum mechanics combined with spectroscopic data should be part of a more thorough analysis, especially when it extends situations atoms monoelectronicpolieletrônicos to describe atoms, because factors such as effective nuclear charge and shielding factor must be taken into consideration, because interactions there is inside an atom, described by a set ofquantum numbers, sometimes not taken into account

Globally solvable systems of complex vector fields

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the connectedness of all sublevel and superlevel sets of the primitive of a certain 1-form in the minimal covering space.

Stresses and stability of a mine paste fill

Se describe el comportamiento de los rellenos de pasta de las cámaras primarias de la mina de Aguas Teñidas y se calcula la resistencia que deben tener dichos rellenos para que no se desmoronen las paredes de los mismos que quedan expuestas al extraer las cámaras secundarias.Abstract:This article presents the study carried out at an underground mine to understand the stress distribution in the paste fills and to calculate the stability of the paste walls. The mine is operated using sublevel stopes. Three-dimensional numerical models designed with the FLAC 3D software are used to study the distribution of the vertical stresses in the paste. The numerical models have demonstrated that an arc-like effect is produced in the paste fills of the primary stopes. This effect relieves the vertical stresses and increases the stability of the exposed paste wall fill. Based on the results of the numerical models, in the 30m high secondary stopes, the arc effect starts to be evident only in paste walls with a width/height ratio lower than 0.8. 3-D calculations show that the use of Mitchell, R. J. et al. (1982) formula may be risky when estimating the fill stability in secondary stopes.

Estudio de las distribuciones tensionales y de las resistencias de los rellenos de pasta de la mina subterránea de Aguas Teñidas (Huelva)

This thesis presents the study carried out at an underground mine to understand the stress distribution in the paste fills and to calculate the stability of the paste walls in the primary and secondary stopes. The mine is operated using sublevel stopes and fan blasting. The primary and secondary stopes are 20m wide, 30m high and between 20 and 60m long. Three-dimensional numerical models designed with the FLAC 3D software programme are used to study the distribution of the vertical stresses in the paste walls exposed in the primary and secondary stopes, and their evolution as the mining advance increases. The numerical models have demonstrated that an arc-like effect is produced in the paste fills of the primary stopes, that is, those which have either lateral walls in mineral or rock. This effect relieves the vertical stresses and increases the stability of the exposed paste wall fill. From the study, it is deduced that in this type of stope, the fill stability can be calculated using the formula established by Mitchell, (Mitchell, Olsen, and Smith 1982, 14-28). Based on the results of the numerical models, in the 30m high secondary stopes, the arc effect starts to be evident only in paste walls with a width/height ratio lower than 0.7. 3-D calculations show that the use of Mitchell formula may be risky when estimating the fill stability in secondary stopes. Therefore, in these cases, the traditional two-dimensional method for calculating the stability of vertical slopes on cohesive saturated soils in the short term should be used. However this method may give conservative results for paste walls in secondary stopes with a width/height ratio below 0.5. RESUMEN Esta Tesis presenta el estudio realizado en la mina subterránea de Aguas Teñidas (Huelva, España) para comprender la distribución de tensiones en los rellenos de pasta y calcular la estabilidad de las paredes de pasta en las cámaras primarias y secundarias. El método de explotación utilizado en esta mina es el de cámaras con subniveles y voladura en abanico. Las cámaras primarias y secundarias tienen una anchura de 20 m, una altura de 30 m y una longitud variable entre 20 y 60 m. Mediante modelos numéricos tridimensionales realizados con el programa FLAC 3D se ha estudiado la distribución de las tensiones verticales en las paredes de pasta que quedan expuestas en las cámaras primarias y secundarias, y su evolución a medida que aumenta la superficie explotada. La modelización numérica ha puesto de manifiesto que se produce efecto arco en los rellenos de pasta de las cámaras primarias, o sea, aquellas que tienen ambos hastiales en mineral o en roca. Este efecto aligera las tensiones verticales y aumenta la estabilidad del relleno de la pared de pasta expuesta. De acuerdo con los resultados de los modelos numéricos, en las cámaras secundarias de 30 m de alto, el efecto arco empieza a manifestarse solamente en las paredes de pasta de relación anchura/altura menor de 0,7. Los cálculos realizados en tres dimensiones indican que la fórmula de Mitchell (Mitchell, Olsen, y Smith 1982, 14-28) puede resultar arriesgada para estimar la estabilidad del relleno en este tipo de cámaras. Por consiguiente, se recomienda utilizar en estos casos el método que tradicionalmente se ha empleado para calcular la estabilidad de taludes verticales en suelos cohesivos a corto plazo, en dos dimensiones. Aunque este método puede resultar conservador para paredes de pasta de cámaras secundarias con una relación anchura/altura inferior a 0,5. Para usar relleno de pasta para el sostenimiento en minería subterránea hay que tener en cuenta el cálculo de los parámetros de diseño, optimización de la mezcla, cualidades de bombeo y la operación de transporte al interior de la mina. Los gastos de ésta operación minera son importantes ya que pueden representar hasta de 20%.