L. G. Ferreira Filho

Coherent particle production at relativistic heavy-ion colliders including strong absorption effects

Abstract Photon-photon fluxes are calculated for relativistic heavy-ion collisions. Special care is taken of nuclear absorption effects, they reduce the γ fluxes and also lead to a polarization effect. Lepton pair, meson and Higgs-boson production are considered, at energies relevant for RHIC and LHC (or SSC). Due to the coherency effect, comparatively large cross sections are obtained. This opens up interesting possibilities for γ physics at relativistic heavy-ion colliders.

Sound waves and solitons in hot and dense nuclear matter

Abstract Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by “radiation”. Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase.

Quantization of Friedmann-Robertson-Walker spacetimes in the presence of a negative cosmological constant and radiation

The quantization of the Friedmann-Robertson-Walker spacetime in the presence of a negative cosmological constant was used in a recent paper to conclude that there are solutions that avoid singularities (big bang-big crunch) at the quantum level. We show that a proper study of their model does not indicate that it prevents the occurrence of singularities at the quantum level, in fact the quantum probability of such event is larger than the classical one. Our numerical simulations based on the powerful variational sinc collocation method (VSCM) also show that the precision of the results of that paper is much lower than the 20 significant digits reported by the authors.

Tunneling probability for the birth of an asymptotically de Sitter universe

In the present work, we quantize a closed Friedmann-Robertson-Walker model in the presence of a positive cosmological constant and radiation. It gives rise to a Wheeler-DeWitt equation for the scale factor which has the form of a Schrodinger equation for a potential with a barrier. We solve it numerically and determine the tunneling probability for the birth of a asymptotically DeSitter, inflationary universe, initially, as a function of the mean energy of the initial wave-function. Then, we verify that the tunneling probability increases with the cosmological constant, for a fixed value of the mean energy of the initial wave-function.

Nonlinear waves in a quark gluon plasma

We study the propagation of perturbations in the quark gluon plasma. This subject has been addressed in other works and in most of the theoretical descriptions of this phenomenon the hydrodynamic equations have been linearized for simplicity. We propose an alternative approach, also based on hydrodynamics but taking into account the nonlinear terms of the equations. We show that these terms may lead to localized waves or even solitons. We use a simple equation of state for the QGP and expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We solve them numerically and find that localized perturbations can propagate for long distances in the plasma. Under certain conditions our solutions mimic the propagation of Korteweg-de Vries solitons.

Symplectic method in quantum cosmology

E. V. Corrêa Silva∗,1 G. A. Monerat†,1 G. Oliveira-Neto‡,1 C. Neves§,1 and L. G. Ferreira Filho¶2 Departamento de Matemática e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra, Km 298, Pólo Industrial, CEP 27537-000, Resende-RJ, Brazil. Departamento de Mecânica e Energia, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra, Km 298, Pólo Industrial, CEP 27537-000, Resende-RJ, Brazil. (Dated: March 24, 2009)

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

We study linear and nonlinear wave propagation in a dense and cold hadron gas and also in a cold quark gluon plasma, taking viscosity into account and using the Navier-Stokes equation. The equation of state of the hadronic phase is derived from the nonlinear Walecka model in the mean field approximation. The quark gluon plasma phase is described by the MIT equation of state. We show that in a hadron gas viscosity strongly damps wave propagation and also hinders shock wave formation. This marked difference between the two phases may have phenomenological consequences and lead to new QGP signatures.

AN EARLY UNIVERSE MODEL WITH STIFF MATTER AND A COSMOLOGICAL CONSTANT

In the present work, we study the quantum cosmology description of a Friedmann-Robertson-Walker model in the presence of a stiff matter perfect fluid and a negative cosmological constant. We work in the Schutzs variational formalism and the spatial sections have constant negative curvature. We quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this model the states are bounded therefore we compute the discrete energy spectrum and the corresponding eigenfunctions. In the present work, we consider only the negative eigenvalues and their corresponding eigenfunctions. This choice implies that the energy density of the perfect fluid is negative. A stiff matter perfect fluid with this property produces a model with a bouncing solution, at the classical level, free from an initial singularity. After that, we use the eigenfunctions in order to construct wave packets and evaluate the time-dependent expectation value of the scale factor. We find that it oscillates between maximum and minimum values. Since the expectation value of the scale factor never vanishes, we confirm that this model is free from an initial singularity, also, at the quantum level.

Spectral: Solving Schroedinger and Wheeler–DeWitt equations in the positive semi-axis by the spectral method

Abstract The Galerkin spectral method can be used for approximate calculation of eigenvalues and eigenfunctions of unidimensional Schroedinger-like equations such as the Wheeler–DeWitt equation. The criteria most commonly employed for checking the accuracy of results is the conservation of norm of the wave function, but some other criteria might be used, such as the orthogonality of eigenfunctions and the variation of the spectrum with varying computational parameters, e.g. the number of basis functions used in the approximation. The package Spectra, which implements the spectral method in Maple language together with a number of testing tools, is presented. Alternatively, Maple may interact with the Octave numerical system without the need of Octave programming by the user. Program summary Program title: Spectral Catalogue identifier: AEQQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEQQ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 20417 No. of bytes in distributed program, including test data, etc.: 2149904 Distribution format: tar.gz Programming language: Maple, GNU Octave 3.2.4 Computer: Any supporting Maple Operating system: Any supporting Maple RAM: About 4 Gbytes Classification: 1.9, 4.3, 4.6. Nature of problem: Numerical solution of Schrodinger-like eigenvalue equations (especially the Wheeler–DeWitt equation) in the positive semi-axis Solution method: The unknown wave function is approximated as a linear combination of a suitable set of functions, and the continuous eigenvalue problem is mapped into a discrete (matricial) eigenvalue problem Restrictions: Limitations are due to memory usage only Unusual features: The package may not work properly in older versions of Maple, due to a bug in that CAS; for that reason an interface with the GNU Octave system is provided, requiring no user intervention or Octave programming during calculations Running time: Seconds to hours, depending on the number of basis functions used and on the complexity of the potential used

Korteveg-de Vries solitons in a cold quark-gluon plasma

The relativistic heavy ion program developed at RHIC and now at LHC motivated a deeper study of the properties of the quark gluon plasma (QGP) and, in particular, the study of perturbations in this kind of plasma. We are interested on the time evolution of perturbations in the baryon and energy densities. If a localized pulse in baryon density could propagate throughout the QGP for long distances preserving its shape and without loosing localization, this could have interesting consequences for relativistic heavy ion physics and for astrophysics. A mathematical way to proove that this can happen is to derive (under certain conditions) from the hydrodynamical equations of the QGP a Korteveg-de Vries (KdV) equation. The solution of this equation describes the propagation of a KdV soliton. The derivation of the KdV equation depends crucially on the equation of state (EOS) of the QGP. The use of the simple MIT bag model EOS does not lead to KdV solitons. Recently we have developed an EOS for the QGP which includes both perturbative and non-perturbative corrections to the MIT one and is still simple enough to allow for analitycal manipulations. With this EOS we were able to derive a KdV equation for the cold QGP.