Dark energy parametrizations and their effect on dark halos

There are a plethora of dark energy parametrizations that can fit current supernovae Ia data. However, these data are only sensitive to redshifts up to order one. In fact, many of these parametrizations break down at higher redshifts. In this paper we study the effect of dark energy models on the formation of dark halos. We select a couple of dark energy parametrizations which are sensible at high redshifts and compute their effect on the evolution of density perturbations in the linear and non-linear regimes. Using the Press-Schechter formalism we show that they produce distinguishable signatures in the number counts of dark halos. Therefore, future observations of galaxy clusters can provide complementary constraints on the behaviour of dark energy.

THE REDUCTIVE PERTURBATION METHOD AND THE KORTEWEG-DE VRIES HIERARCHY

By using the reductive perturbation method of Taniuti with the introduction of an infinite sequence of slow time variables tau(1), tau(3), tau(5), ..., we study the propagation of long surface-waves in a shallow inviscid fluid. The Korteweg-de Vries (KdV) equation appears as the lowest order amplitude equation in slow variables. In this context, we show that, if the lowest order wave amplitude zeta(0) satisfies the KdV equation in the time tau(3), it must satisfy the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1), With n = 2, 3, 4,.... AS a consequence of this fact, we show with an explicit example that the secularities of the evolution equations for the higher-order terms (zeta(1), zeta(2),...) of the amplitude can be eliminated when zeta(0) is a solitonic solution to the KdV equation. By reversing this argument, we can say that the requirement of a secular-free perturbation theory implies that the amplitude zeta(0) satisfies the (2n+1)th order equation of the KdV hierarchy in the time tau(2n+1) This essentially means that the equations of the KdV hierarchy do play a role in perturbation theory. Thereafter, by considering a solitary-wave solution, we show, again with an explicit, example that the elimination of secularities through the use of the higher order KdV hierarchy equations corresponds, in the laboratory coordinates, to a renormalization of the solitary-wave velocity. Then, we conclude that this procedure of eliminating secularities is closely related to the renormalization technique developed by Kodama and Taniuti.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Casimir effect for the scalar field under Robin boundary conditions: a functional integral approach

In this work we show how to define the action of a scalar field such that the Robin boundary condition is implemented dynamically, i.e. as a consequence of the stationary action principle. We discuss the quantization of that system via functional integration. Using this formalism, we derive an expression for the Casimir energy of a massless scalar field under Robin boundary conditions on a pair of parallel plates, characterized by constants c(1) and c(2). Some special cases are discussed; in particular, we show that for some values of cl and c(2) the Casimir energy as a function of the distance between the plates presents a minimum. We also discuss the renormalization at one-loop order of the two-point Green function in the philambda(4) theory subject to the Robin boundary condition on a plate.

Multipolar polarizabilities of the sodium atom by a variationally stable procedure

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Ladder operators for subtle hidden shape-invariant potentials

Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics, we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance.

Generalizing the soldering procedure

We start this work by revisiting the problem of the soldering of two chiral Schwinger models of opposite chiralities. We verify that, different from what one can conclude from the current literature, the usual sum of these models is, in fact, gauge invariant and corresponds to a composite model, where the component models are the vector and axial Schwinger models. As a consequence, we reinterpret this formalism as a kind of degree of freedom reduction mechanism. This result has led us to discover a second soldering possibility giving rise to the axial Schwinger model. This new result is seemingly rather general. We explore it here in the soldering of two Maxwell-Chern-Simons theories with different masses.

A NEW CONSTRAINTS SEPARATION FOR THE ORIGINAL D=10 MASSLESS SUPERPARTICLE

We study the problem of covariant separation between first and second class constraints for the D = 10 Brink-Schwarz superparticle. Opposite to the supersymmetric light-cone frame separation, we show here that there is a Lorentz covariant way to identify the second class constraints such that, however, supersymmetry is broken. Consequences for the D = 10 superstring are briefly discussed.

Hamilton-Jacobi formulation for singular systems with second-order Lagrangians

Recently, the Hamilton-Jacobi formulation for first-order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi formulation for singular systems with second-order Lagrangians and apply this new formulation to Podolsky electrodynamics, comparing with the results obtained through Dirac's method.

STOCHASTIC QUANTIZATION AND 1/N EXPANSION

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudo-differential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld-Sokolov realization.

Kinetic aspects of ion exchange in KhFek[Fe(CN)(6)](l)center dot mH(2)O compounds: A combined electrical and mass transfer functions approach

The present paper quantifies and develops the kinetic aspects involved in the mechanism of interplay between electron and ions presented elsewhere(1) for KhFek[Fe(CN)(6)](l)center dot mH(2)O (Prussian Blue) host materials. Accordingly, there are three different electrochemical processes involved in the PB host materials: H3O+, K+, and H+ insertion/extraction mechanisms which here were fully kinetically studied by means of the use of combined electronic and mass transfer functions as a tool to separate all the processes. The use of combined electronic and mass transfer functions was very important to validate and confirm the proposed mechanism. This mechanism allows the electrochemical and chemical processes involved in the KhFek[Fe(CN)(6)](l)center dot mH(2)O host and Prussian Blue derivatives to be understood. In addition, a formalism was also developed to consider superficial oxygen reduction. From the analysis of the kinetic processes involved in the model, it was possible to demonstrate that the processes associated with K+ and H+ exchanges are reversible whereas the H3O+ insertion process was shown not to present a reversible pattern. This irreversible pattern is very peculiar and was shown to be related to the catalytic proton reduction reaction. Furthermore, from the model, it was possible to calculate the number density of available sites for each intercalation/deintercalation processes and infer that they are very similar for K+ and H+. Hence, the high prominence of the K+ exchange observed in the voltammetric responses has a kinetic origin and is not related to the amount of sites available for intercalation/deintercalation of the ions.

HELICITY WAVE-FUNCTIONS FOR MASSLESS AND MASSIVE SPIN-2 PARTICLES

Starting from general properties of a spin-2 field, we construct helicity wave functions in the framework of the Weyl-van der Waerden spinor formalism. We discuss here the cases of massless and massive spin-2 particles.

Spectroscopic properties of Er3+ in oxysulfide glasses

Er3+ -containing gallium-lanthanum oxysulfide glasses have been prepared from Ga2O3 and La2S3 in a sulfur/argon reactive atmosphere. The samples have been characterized by absorption and emission spectroscopy and IR emission kinetics. Er3+ electronic transition intensities have been analyzed in the light of the Judd-Ofelt formalism, and quantum efficiencies evaluated for the Er3+ emission at 1.5 and 2.7 mum. The results so obtained suggest that these glasses display favorable properties concerning IR optical applications. (C) 2002 Elsevier B.V. B.V. All rights reserved.