Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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

Quadratic gravity in (2+1)D with a topological Chern-Simons term

Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chem-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity.

Can one cure the nommitarity of three-dimensional quadratic gravity using a topological Chern-Simons term?

Quadratic gravity in (2+1)D is nonunitarity at the tree level. When a topological Chern-Simons term is added to this theory, the harmless massive scalar mode of the former gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin-2. Therefore, unlike what it is claimed in the literature, quadratic Chern-Simons gravity in (2+1)D is nonunitary at the tree level.

The quadratic spinor Lagrangian, axial torsion current and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field-Weyl, Majorana, flagpole, or flag-dipole spinor fields-yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

Linear to quadratic crossover of Cooper-pair dispersion relation

Cooper pairing is studied in three dimensions to determine its binding energy for all coupling using a general separable interfermion interaction. Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM). A coupling-independent linear term in the CMM dominates the pair excitation energy in weak coupling and/or high fermion density, while the more familiar quadratic term prevails only in the extreme low-density (i.e., vacuum) limit for any nonzero coupling. The linear-to-quadratic crossover of the CP dispersion relation is analyzed numerically, and is expected to play a central role in a model of superconductivity (and superfluidity) simultaneously accommodating a Bardeen-Cooper-Schrieffer condensate as well as a Bose-Einstein condensate of CP bosons. (C) 2001 Elsevier B.V. B,V. All rights reserved.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

The addition of a topological Chern-Simons term to three-dimensional higher-derivative gravity is not a good therapy to cure the nonunitarity of the aforementioned theory. Moreover, R+R-2 gravity in (2+1)D, which is unitary at the tree level, becomes tree-level nonunitary when it is augmented by the abovementioned topological term. Therefore, unlike what is claimed in the literature, topological higher-derivative gravity in (2+1)D is not tree-level unitary and neither is topological three-dimensional R+R-2 gravity.

Light deflection and quadratic gravity

We study the bending of light caused by a static gravitational field generated by a localized material source in the context of quadratic gravity. Our calculation shows that for light rays passing close to the Sun the deflection Phi lies in the interval 0 < < 1.75. A tree-level approach to the same issue tells us that the vacuum concerning quadratic gravity is a dispersive medium. Nom Phi is energy dependent and ranges from 0(+) to 1.75(-) arcsec.

Construction of time-dependent dynamical invariants: A new approach

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

Efeito da Idade da Vaca ao Parto e da Data Juliana de Nascimento sobre Características Pré-desmama de Bezerros da Raça Gir

Objetivou-se com este trabalho estimar a influência da idade da vaca ao parto (IDV) e da data juliana de nascimento (DJN) sobre o peso à desmama (PD) e a média do ganho diário no período pré-desmama (GMD) de bezerros Gir, determinando fatores de correção para estes efeitos. Foram analisados 10.685 e 18.339 dados de PD e GMD de bezerros Gir, provenientes do Arquivo da Associação Brasileira dos Criadores de Zebu (ABCZ), pertencentes a 1229 e 1979 grupos contemporâneos (GC), respectivamente. PD e GMD foram pré-ajustados para o efeito da idade do bezerro à desmama. O efeito de IDV sobre PD e GMD foi modelado como polinômio segmentado quadrático-quadrático-quadrático, com nós, ou pontos de junção aos 4,1; 12,7 e 4,0; 8,2 anos, respectivamente, para machos e como polinômio segmentado quadrático-quadrático, com nó, ou ponto de junção aos 3,8 anos, para fêmeas sobre as duas características. A DJN foi modelada como um polinômio segmentado quadrático-quadrático com nó aos 126 dias para PD e 167 dias para GMD. Os resultados mostraram que a determinação dos fatores de correção para IDV deve ser feita, separadamente, para machos e fêmeas e, para DJN, deve-se considerar cada estação do ano, para que as diferenças entre elas sejam bem observadas. Os fatores de correção para o efeito da idade da vaca variaram de 0,94750 a 1,08033 sobre PD e 0,91714 a 1,07689 sobre GMD, para machos, e de 0,90937 a 1,07415 sobre PD e 0,96055 a 1,14007 sobre GMD, para fêmeas. Para o efeito de DJN, a amplitude foi de 0,9256 a 1,0340 sobre PD e 0,9112 a 1,0551 sobre GMD.

Approximate analytical states of a polynomial potential: an example of symmetry restoration

An approximate analytical expression for the first two eigenvalues of the Schrodinger equation for the potential V(x) = Ax(4) + Bx(2) is achieved by using the Symanzik scaling symmetry. A kind of symmetry restoration when one of the potential parameters changes conveniently is observed. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Bound states of the Dirac equation for a class of effective quadratic plus inversely quadratic potentials

The Dirac equation is exactly solved for a pseudoscalar linear plus Coulomb-like potential in a two-dimensional world. This sort of potential gives rise to an effective quadratic plus inversely quadratic potential in a Sturm-Liouville problem, regardless the sign of the parameter of the linear potential, in sharp contrast with the Schrodinger case. The generalized Dirac oscillator already analyzed in a previous work is obtained as a particular case. (C) 2004 Elsevier B.V. All rights reserved.