The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Quasi-homologous spherically symmetric branes and their symmetry breaking

We revisit the dynamical system-based approach of spherically symmetric vacuum braneworlds, pointing out and studying the existence of a transcritical bifurcation as the dark pressure parameter changes its sign, we analyze some consequences of not discard the brane cosmological constant. For instance, it is noteworthy that the existence of an isothermal state equation between the dark fluid parameters cannot be obtained via the requirement of a quasi-homologous symmetry of the vacuum. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

PT-symmetric coupler with chi((2)) nonlinearity

We introduce the notion of a PT-symmetric dimer with a chi((2)) nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain and loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first-or the second-harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur, including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.

Classic tests of General Relativity described by brane-based spherically symmetric solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymmetric and Symmetric Triazenido Cyclopalladated Complexes: Synthesis, Structural Analysis and DFT Calculations

The reaction of [Pd{dmba}(l-N3)]2 (dmba = N,N-dimethylbenzylamine) with 1-(2-fluorophenyl)-3-(4- nitrophenyl)triazenido (L1 ) or 1,3-bis(4-nitrophenyl)triazenido (L2 ) anions, in methanol, and subsequent treatment with pyridine (py) allows the preparation of the corresponding cyclopalladated compounds [Pd(dmba)(L1 )(py)] (1) and [Pd(dmba)(L2 )(py)]py (2). The acentric mononuclear entities of (1) and (2) are connected by weak intermolecular non-classical CAHC hydrogen bonds, which results in 2-D arrangements by translation, along the [1 0 0] and [0 01] crystallographic directions, respectively.

Bounds for the zeros of symmetric kravchuk polynomials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrodinger equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integrable deformations of strings on symmetric spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conservation laws for Z(N) symmetric quantum spin models and their exact ground state energies

We derive an infinite set of conserved charges for some Z(N) symmetric quantum spin models by constructing their Lax pairs. These models correspond to the Potts model, Ashkin-Teller model and the particular set of self-dual Z(N) models solved by Fateev and Zamolodchikov [6]. The exact ground state energy for this last family of hamiltonians is also presented. © 1986.