We apply the generalized Zeta function method to compute the Casimir energy and pressure between an unusual pair of parallel plates at finite temperature, namely, a perfectely conducting plate (ǫ → ∞) and an infinitely permeable one (µ → ∞). The high and low temperature limits of these quantities are discussed. Relationships between high and low temperature limits for the free energy are established by means of a modified version of the temperature inversion symmetry.

We compute the Casimir pressure between an unusual pair of parallel plates, namely, a perfectly conducting plate ! 1 and an in nitely permeable one ! 1 with the generalized -function method. The result for this problem, which has been rarely discussed in the literature, is a repulsive Casimir force. The -function method provides a very compact and economic way of obtaining the nal result.Since Casimir's paper 1 on the attraction of two neutral parallel perfectly conducting plates due to the vacuum uctuations of the electromagnetic eld, a considerable amount o f w ork has been done on this subject, varying from the application of alternative techniques to the exploration of new geometries and theories. Excellent reviews as well as a large list of relevant references on this subject can be found in the work of Plunien et al 2 and in the book by Mostepanenko and Trunov 3 .The rst experimental test of Casimir's prediction was made by Sparnaay 4 only in 1958. However, the accuracy of the results was far from being reasonable: approximately one hundred percent of error. Since then, experiments involving dielectrics have been done, but only four decades after Sparnaay's work an experiment of the Casimir force between metals was repeated: in 1997, Lamoreaux 5 made an experiment with a slightly di erent geometry a spherical metallic lens and a at metal plate where theory and the experimental data agree within a few percents. More recently, another experiment with metals was performed by U. Mohideen and A. Roy 6 . Using an atomic force microscope they measured the Casimir force between a metallized sphere of diameter equal to 196m and a at metal plate for separations from 0; 1m t o 0 ; 9m. They showed that the experimental data are in very good agreement with the theoretical predictions. May be this is one of the most striking results of quantum eld theory once it is a macroscopic measurable manifestation of the quantum vacuum. Instead of paying attention to the sources the perfect conducting plates, Casimir's approach for this problem consisted basically in computing the interacting energy between the plates as the regularized di erence between the zero point energies with and without the boundary conditions dictated by the physical situation perfectly conductor character of the plates. In fact, the great novelty of Casimir's paper of 1948 was not the fact that two neutral objects attracted each other 1 , but the simplicity of the method to do it in the context of quantum eld theory. However, since Casimir's work, many other techniques were developed which m a y be more appropriate depending on the physical situation under study. In particular, methods of computing e ective actions are in general very powerful for our purposes.We shall be concerned here with one of these methods, namely, the so called generalized -function method. In this communication we shall apply it to the unusual case of a pair of parallel plates, where one of them is perfectly conducting ! 1 , while the other is in nitely permeable ! 1 . This probl...

It is a well known fact that non-trivial boundary conditions affect the interaction between atoms and the always present quantized electromagnetic field. In this paper, we focus on how the spontaneous emission rate of a given excited atom is altered when placed inside a perfectly conducting wedge. We begin by briefly presenting the formalism on which our calculations are founded, proceeding then to a long but straightforward calculation of the transition rate. We present results for a general atom but, for the sake of simplicity, we narrow them down to an effective two-level system in our numerical investigations. From these we conclude that the results are physically sound.Comment: 10 pages, version replaced to match the published on

We consider the interaction between an electrically polarizable atom in its fundamental state and a wedge constituted by two semi-infinite perfectly conducting plates. Using a formalism based on a master equation, we compute the dispersion force on the atom for both retarded and non-retarded regimes.

ResumoDesde 2008, por lei (Lei 11.645/08), a cultura indígena deve ser inserida no currículo da Educação Básica brasileira. Entretanto, propostas de inclusão fundamentadas na etnomatemática são escassas. O presente trabalho traz uma proposta de recurso didático tecnológico no contexto da etnomatemática xavante: um jogo sobre probabilidade condicional chamado "Adivinhe o número xavante". O jogo foi desenvolvido na plataforma Scratch, concebida pelo Massachusetts Institute of Technology (MIT) para promover a aprendizagem de programação por crianças maiores de oito anos. O jogo pode ser usado por docentes da Educação Básica para os alunos conhecerem mais sobre a cultura indígena brasileira e a Matemática xavante de forma lúdica, ao mesmo tempo em que estimula o raciocínio lógico-quantitativo e introduz de modo informal conceitos de probabilidade condicional.Palavras-chave: Etnomatemática. Cultura Indígena. Xavante. Jogo. Probabilidade Condicional. AbstractSince 2008, Federal Law 11.645/08 established that indigenous cultures should be inserted in the Brazilian Basic Education curriculum. However, inclusion proposals of indigenous traits based on ethnomathematics are scarce. This paper suggests the use of a technological teaching resource in the context of Xavante etnomathematics: a game exploring conditional probability called "Guess the Xavante number". The game developed on the Scratch platform, and created by Massachusetts Institute of Technology (MIT), promotes computer programing learning among children over eight years old. The game can be used by middle and high school teachers to promote * Especialista em Novas Tecnologias no Ensino da Matemática pela Universidade Federal Fluminense (UFF), Niterói, Rio de Janeiro, Brasil. Professor da Secretária de Educação do Estado do Rio de Janeiro (SEEDUC/RJ), Rio de Janeiro, RJ, Brasil. Endereço para correspondência: LANTE -Rua Mário dos Santos Braga, s/n,