Relativistic particle dynamics in D=2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and tau-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables lambda(alpha) show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.

Confusing the extragalactic neutrino flux limit with a neutrino propagation limit

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

Particle creation due to tachyonic instability in relativistic stars

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

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Limit between stages I and II of a seed imbibition curve

O conhecimento das fases de absorção de água das diferentes espécies é importante em pesquisas objetivando melhorar a qualidade das sementes, utilizando tratamentos como condicionamento osmótico, pré-hidratação e uso de bioreguladores. O objetivo do presente trabalho foi estabelecer uma metodologia para determinar o limite entre a primeira e a segunda fase do processo, considerando o modelo W = f(t) - (a - w0)exp(-kt), utilizando testes estatísticos. O limite entre as duas primeiras fases do processo de absorção de água pelas sementes, foi determinado utilizando-se a distribuição assintótica de uma função de estimadores. O ponto a partir do qual esta diferença (W*) deixa de ser significativa foi determinado utilizando-se o teste estatístico T de Student. Para os dados utilizados como exemplo, tem-se o modelo ou =(0,434 + 0,00162 t) - (0,434 - w o)exp(-0,121 t), com r² = 0,98 e W* = (0,434 - w o) exp(-0,121 t). O valor de t encontrado (27,2 horas) é menor do que o valor determinado, considerando-se como critério para mudança de fase a diferença de 1% entre a assíntota e o valor estimado pelo modelo ajustado. Essa diferença de duas horas corresponde a 0,28% de água absorvida.

The Yang-Lee zeros of the 1D Blume-Capel model on connected and non-connected rings

We carry out a numerical and analytic analysis of the Yang-Lee zeros of the ID Blume-Capel model with periodic boundary conditions and its generalization on Feynman diagrams for which we include sums over all connected and nonconnected rings for a given number of spins. In both cases, for a specific range of the parameters, the zeros originally on the unit circle are shown to depart from it as we increase the temperature beyond some limit. The curve of zeros can bifurcate- and become two disjoint arcs as in the 2D case. We also show that in the thermodynamic limit the zeros of both Blume-Capel models on the static (connected ring) and on the dynamical (Feynman diagrams) lattice tend to overlap. In the special case of the 1D Ising model on Feynman diagrams we can prove for arbitrary number of spins that the Yang-Lee zeros must be on the unit circle. The proof is based on a property of the zeros of Legendre polynomials.

On the amplitudes for non-critical N=2 superstrings

We compute correlation functions in N=2 non-critical superstrings on the sphere. Our calculations are restrained to the (s=0) bulk amplitudes. We show that the four-point function factorizes as a consequence of the non-critical kinematics, but differently from the N=0, 1 cases no extra discrete state appears in the ĉ→1- limit.

Universal scaling in BCS superconductivity in three dimensions in non-s waves

The solutions of a renormalized BCS equation are studied in three space dimensions in s, p and d waves for finite-range separable potentials in the weak to medium coupling region. In the weak-coupling limit, the present BCS model yields a small coherence length ξ and a large critical temperature, T c, appropriate for some high-T c materials. The BCS gap, T c, ξ and specific heat C s(T c) as a function of zero-temperature condensation energy are found to exhibit potential-independent universal scalings. The entropy, specific heat, spin susceptibility and penetration depth as a function of temperature exhibit universal scaling below T c in p and d waves.

Optimized delta expansion for relativistic nuclear models: Renormalization of vacuum fluctuations

We use the optimized linear δ expansion and functional methods to study vacuum contributions in nuclear matter up to the lowest non-trivial order which includes exchange terms. We show that well known results (MFT, RHA and HF) can be easily reproduced when appropriate limits are taken. Neglecting vacuum contributions we explicitly show that the δ expansion goes beyond the traditional loop approximation previously used to study two loop vacuum contributions in nuclear matter. We then evaluate and renormalize vacuum exchange contributions showing that they are numerically very large, as predicted by the ordinary loop approximation.

Quantum vacuum in hot nuclear matter: A non-perturbative treatment

We derive the equation of state for hot nuclear matter using the Walecka model in a non-perturbative formalism. We include here the vacuum polarization effects arising from the nucleon and scalar mesons through a realignment of the vacuum. A ground state structure with baryon-antibaryon condensates yields the results obtained through the relativistic Hartree approximation of summing baryonic tadpole diagrams. Generalization of such a state to include the quantum effects for the scalar meson fields through the σ -meson condensates amounts to summing over a class of multiloop diagrams. The techniques of the thermofield dynamics method are used for the finite-temperature and finite-density calculations. The in-medium nucleon and sigma meson masses are also calculated in a self-consistent manner. We examine the liquid-gas phase transition at low temperatures (≈ 20 MeV), as well as apply the formalism to high temperatures to examine a possible chiral symmetry restoration phase transition.

Pseudospin symmetry and the relativistic harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=5+V and δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit.

Electrochemical reduction and voltammetric determination of diloxanide furoate in non-aqueous medium

The electrochemical reduction of diloxanide furoate (DF) in acetonitrile on glassy carbon electrode was studied in this work. It was observed that DF is reduced after a reversible one-electron transfer followed by an irreversible chemical reaction, diagnosed as C-Cl bond cleavage. Its reduction was followed by linear (LSV), differential pulse (DPV) and square wave voltammetry (SWV). Analytical curves were obtained for DF determination using all the investigated voltammetric techniques. For LSV was obtained a linear range (LR) from 5.0 × 10-4 to 1.0 × 10-2 mol L-1, with detection limit (DL) of 1.5 × 10-4 mol L-1 and sensitivity (S) of 2.1 × 104 μA mol-1 L. The analytical parameters obtained by DPV were: LR = 5.0 × 10-4 to 2.2 × 10-3 mol L-1, DL = 7.8 × 10-5 mol L-1, S = 3.7 × 104 μA mol-1 L. For SWV were obtained a LR = 7.5 × 10-6 to 1.2 × 10 -3 mol L-1, DL = 5.5 × 10-6 mol L -1 and S = 2.8 × 105 μA mol-1 L. Thus, the SWV was the most sensible technique, which can be used for DF determination at low concentration levels. Statistics methods were used to evaluate the analytical procedure, where recovery around to 100% was obtained for all voltammetric techniques. Relative standard deviations were lower than 5.0% (N=5). The obtained t values evaluating all the three voltammetric methods were less than the tabulated ones, indicating that there are no evidences of systematic error. ©2005 Sociedade Brasileira de Química.

Hausdorff dimension for non-hyperbolic repellers II: Da diffeomorphisms

We study non-hyperbolic repellers of diffeomorphisms derived from transitive Anosov diffeomorphisms with unstable dimension 2 through a Hopf bifurcation. Using some recent abstract results about non-uniformly expanding maps with holes, by ourselves and by Dysman, we show that the Hausdorff dimension and the limit capacity (box dimension) of the repeller are strictly less than the dimension of the ambient manifold.

Relativistic particle dynamics in D = 2+1

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and τ-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables λα show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model. © SISSA 2006.