Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]

Currículo-fabulação : a curiosa metamorfose de Francis Tracart

Tem por proposta subversar a escrita linear acadêmica ao (re)fazê-la, vislumbrando as potências e transgressões da literatura menor em seus agenciamentos coletivos, políticos, em seus gaguejos e balbucios, em suas possibilidades de subversão. Fabular a escrita acadêmica e o currículo como ato político e coletivo, como reinvenção da própria língua. Trata da metamorfose de Francis Tracart em sua busca por traçar conceitos,conversações, percepções e afecções. A metodologia se dá por intermédio da pesquisa com os cotidianos e com a cartografia, buscando atentar-se a vozes, entrelinhas, efeitos, tensões, teórico-práticas e saberesfazeres dos sujeitos praticantes dos cotidianos da escola em que se realiza a pesquisa em pé de igualdade com os autores dos livros que permearam o processo de realização do trabalho de pesquisa. Os sujeitos cotidianos, tais como bibliotecária, professoras e alunos de 5º e 6º Ano, orientador, professores e alunos de Pós- Graduação, que participaram do processo de pesquisa, bem como os autores dos livros lidos, se fazem presentes nas vozes, nas falas, nos afectos e nas conversações com leituras, literaturas, currículos, cotidianos, redes de afecções, elementos éticos, estéticos e políticos, espaçostempos, com linhas de fuga, linhas molares e linhas moleculares, com os presentes politemporais,devires, conceitos, metamorfoses, com possíveis e improváveis leituras, fugas e reinvenções do leitor.

Cartografando movimentos curriculares produzidos nas redes de conversações nos encontrosformações do PROEJA/IFES/ES

Problematiza a constituição do currículo (e da “formação docente” no campo curricular), no cotidiano escolar, na dimensão das conversações. Objetiva acompanhar os movimentos curriculares concernentes ao Proeja entre formas e forças complexas no cotidiano do Ifes – campus Venda Nova do Imigrante (VNI). Compõe com as linhas de pensamentos principalmente de Alves (2008, 2010, 2012); Carvalho (2004, 2008a, 2008b, 2009, 2012); Deleuze (1988, 2002, 2010); Deleuze e Guattari (1995); Ferraço (2007, 2008a, 2008b); Garcia (2011); Guattari (1987, 2004, 2012); Kastrup (2009, 2013); Lopes e Macedo (2011); Lopes (2010, 2011); Oliveira (2005, 2009, 2012); Paiva (2004, 2009); Rolnik (1989); e Spinoza (2013), entremeando os conceitos de movimentos e afetos no campo do currículo em redes na relação híbrida com os encontros-formações docente do/no Proeja. Adota a (não) metodologia cartográfica ao acompanhar movimentos curriculares (des)(re)territorializantes nas redes de conversações, especialmente nos encontrosformações: “Rodas de conversas com professores e demais servidores do Proeja”. Utiliza como principais instrumentos metodológicos a observação participante, a gravação das vozes e o registro em diário de campo. Contribui para outros movimentos de pesquisa ao capturar produzir e analisar dados em que se percebe que: ainda que tenha ocorrido um planejamento coletivo, outras temáticas surgiram nos encontros formações (que não se pretendiam engessados e não objetivavam a paralisação dos fluxos que pedem passagem), e tais assuntos puderam ser usados como disparadores para criação de outros movimentos curriculares; as concepções dos professores sobre a “dificuldade/facilidade” em ministrar aulas para o Proeja e os lugares estabelecidos entre estudantes e docentes no processo ensino-aprendizagem não estão relacionados diretamente, em relação de causa e efeito, à disciplina/área de conhecimento específica que ministram, mas aos agenciamentos, aos ligamentos e às rupturas produzidas nas relações com essas redes de saberes fazeres poderes que envolvem múltiplos agentes: docentes, outros servidores, alunos, experiências e encontros múltiplos dentro fora no espaço tempo do Ifes; uma tríade-refrão coopera para a criação de uma fôrma triangular que enfatiza a noção de um padrão em um processo molar enraizado nas árvores do conhecimento: perfil, seleção e nivelamento, contudo, algumas linhas de fuga dissonantes são criadas por entre as fissuras dos pretensos tons harmônicos; as frases “os professores do IF não estão preparados para ministrar aulas para o Proeja” ou “não há formação/qualificação para os docentes se relacionarem com o Proeja” são utilizadas, em alguns discursos, como escudos-argumentos para a opção-política de não oferta de vagas para a modalidade EJA em composição com fios que afirmam tal especificidade da educação básica, dentro da rede federal, como um “favor social”; processos que envolvem a (des)organização da matriz curricular são considerados por alguns participantes como início, “produto” e objetivo das conversas curriculares e provocam tensões que (i)mobilizam, (não) movimentam entre os afetos dos corpos, podendo levar à (não) ação coletiva; a noção de “mercado de trabalho” ainda impera nos discursos, ciclicamente, enquanto início fim das problematizações do currículo do Ensino Médio e da EJA; a expressão “integração curricular” é constantemente usada nos discursos que circulam o campus, no entanto, os sentidos produzidos, as concepções e as teorias curriculares que embasam a noção de “integração” no currículo são bem diversos; não há totalidades nos discursos, não há homogeneização, não foi efetivada nenhuma coesão/única voz representante (e esse também não era o objetivo desta pesquisa); ainda que o tema da roda se propusesse às conversas curriculares do/no Proeja, nesses encontros, os participantes manifestaram a necessidade de intensificar os movimentos produzidos nas rodas visando à discussão dos currículos textos de todos os cursos e modalidades ofertados pelos campus VNI e na intensificação de espaços para trocas de experiências curriculares cotidianas; na potencialização das diferenças como possibilidades de inventividade nos encontros-formações docente e nas danças curriculares que envolvem diversas relações de aprendizagem no Ifes, algumas experimentações foram produzidas, entre afetos, criando composições(des)(re)territorializantes e ressonando com movimentos que não se restringiram às rodas de conversas, contudo, enredaram-se em fios de outros espaços tempos do campus em tentativas de propagações de currículos multidão.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Cylindrically symmetric models of gravitational collapse to black holes: a short review

We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.

The metaphysics of quantum gravity : a causal approach

The dissertation investigates some relevant metaphysical issues arising in the context of spacetime theories. In particular, the inquiry focuses on general relativity and canonical quantum gravity. A formal definition of spacetime theory is proposed and, against this framework, an analysis of the notions of general covariance, symmetry and background independence is performed. It is argued that many conceptual issues in general relativity and canonical quantum gravity derive from putting excessive emphasis on general covariance as an ontological prin-ciple. An original metaphysical position grounded in scientific essential- ism and causal realism (weak essentialism) is developed and defended. It is argued that, in the context of general relativity, weak essentialism supports spacetime substantivalism. It is also shown that weak essentialism escapes arguments from metaphysical underdetermination by positing a particular kind of causation, dubbed geometric. The proposed interpretive framework is then applied to Bohmian mechanics, pointing out that weak essentialism nicely fits into this theory. In the end, a possible Bohmian implementation of loop quantum gravity is considered, and such a Bohmian approach is interpreted in a geometric causal fashion. Under this interpretation, Bohmian loop quantum gravity straightforwardly commits us to an ontology of elementary extensions of space whose evolution is described by a non-local law. The causal mechanism underlying this evolution clarifies many conceptual issues related to the emergence of classical spacetime from the quantum regime. Although there is as yet no fully worked out physical theory of quantum gravity, it is argued that the proposed approach sets up a standard that proposals for a serious ontology in this field should meet.

On fast-decodable space-time block codes

We focus on full-rate, fast-decodable space–time block codes (STBCs) for 2 x 2 and 4 x 2 multiple-input multiple-output (MIMO) transmission. We first derive conditions and design criteria for reduced-complexity maximum-likelihood (ML) decodable 2 x 2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reduced-complexity 4 x 2 STBC, and show that it outperforms all previously known codes with certain constellations.

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Diracs method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Gauge transformations in Einstein-Yang-Mills theories

We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the YangMills type coupled with Einsteins general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure YangMills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the spacetime metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer. 2000 American Institute of Physics.

Diffusion of passive scalars under stochastic convection

The diffusion of passive scalars convected by turbulent flows is addressed here. A practical procedure to obtain stochastic velocity fields with well¿defined energy spectrum functions is also presented. Analytical results are derived, based on the use of stochastic differential equations, where the basic hypothesis involved refers to a rapidly decaying turbulence. These predictions are favorable compared with direct computer simulations of stochastic differential equations containing multiplicative space¿time correlated noise.

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.