Calculating error bars for neutrino mixing parameters

One goal of contemporary particle physics is to determine the mixing angles and mass-squared differences that constitute the phenomenological constants that describe neutrino oscillations. Of great interest are not only the best fit values of these constants but also their errors. Some of the neutrino oscillation data is statistically poor and cannot be treated by normal (Gaussian) statistics. To extract confidence intervals when the statistics are not normal, one should not utilize the value for chisquare versus confidence level taken from normal statistics. Instead, we propose that one should use the normalized likelihood function as a probability distribution; the relationship between the correct chisquare and a given confidence level can be computed by integrating over the likelihood function. This allows for a definition of confidence level independent of the functional form of the !2 function; it is particularly useful for cases in which the minimum of the !2 function is near a boundary. We present two pedagogic examples and find that the proposed method yields confidence intervals that can differ significantly from those obtained by using the value of chisquare from normal statistics. For example, we find that for the first data release of the T2K experiment the probability that chisquare is not zero, as defined by the maximum confidence level at which the value of zero is not allowed, is 92%. Using the value of chisquare at zero and assigning a confidence level from normal statistics, a common practice, gives the over estimation of 99.5%.Comment: 9 pages, 6 figure

Qubits entanglement dynamics modified by an effective atomic environment

We study entanglement dynamics of a couple of two-level atoms resonantly interacting with a cavity mode and embedded in a dispersive atomic environment. We show that in the absence of the environment the entanglement reaches its maximum value when only one exitation is involved. Then, we find that the atomic environment modifies that entanglement dynamics and induces a typical collapse-revival structure even for an initial one photon Fock state of the field.Comment: eight pages, two figure include

Electronic structure of the double perovskite Ba2Er(Nb,Sb)O 6

In this work, we present a detailed study of the structural and the electronic structure of the double perovskite Ba2Er(Nb,Sb)O 6. All calculations were performed with the Full-Potential Linear Augmented Plane Wave method (FP-LAPW) based on the Density Functional Theory (DFT). From the minimization of energy as a function of volume using the Murnaghan's state equation has been obtained the equilibrium lattice parameter and the bulk modulus of these compounds. The study of the electronic structure was based in the analysis of the electronic density of states (DOS), and the density of charge, showing that these compounds have a total magnetic moment of 3.0 μB per formula unit due to Er atoms.Fil: Gil Rebaza, Arles Víctor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Deluque Toro, Crispulo Enrique. Universidad Popular del Cesar; ColombiaFil: Téllez Landínez, D. A. Universidad Nacional de Colombia; ColombiaFil: Roa Rojas, J.. Universidad Nacional de Colombia; Colombi

Dificultad en los problemas combinatorios en estudiantes con preparación matemática avanzada

En este trabajo se presenta un estudio sobre la dificultad que la resolución de problemas combinatorios simples y compuestos supone para los alumnos de cuarto y quinto curso de la licenciatura de Matemáticas. Se propuso a una muestra de 91 estudiantes un cuestionario con 13 problemas combinatorios, de los cuales 11 se resolvían con una única operación combinatoria y dos eran problemas combinatorios compuestos de dos operaciones. Las variables controladas en el cuestionario son: la operación combinatoria, esquema combinatorio y naturaleza de los objetos combinados. Los resultados son analizados en función de estas variables y se comparan con los de una muestra de estudiantes de Primer Curso de Bachillerato, con y sin instrucción combinatoria. observamos una dificultad elevada de estos problemas, que en algunos casos no difiere de la de los alumnos de Bachillerato y el efecto de algunas de las variables de tarea. Todos estos resultados nos sirven para replanteamos los objetivos de la enseñanza de la combinatoria