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Recent measurements at RHIC suggest that a nearly perfect fluid of quarks and gluons is produced in A A collisions. Moreover the passage of supersonic partons through this medium seems to produce waves. These waves might pile up and form Mach cones, which would manifest themselves in the so called away-side jets, forming a broad structure in the angular distribution of the particles recoiling against a trigger jet of moderate energy. In most of the theoretical descriptions of these phenomena, the hydrodynamic equations are linearized for simplicity. We propose an alternative explanation for the observed broadening of the away-side peak. It is based on hydrodynamics but it is a consequence of the non-linearities of the equations, which instead of simple waves may lead to localized waves or even solitons.We investigate in detail the consequences of including the non-linear terms. 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 mimick the propagation of Korteweg -de Vries solitons.

In the present work, we quantize three Friedmann-Robertson-Walker models in the presence of a negative cosmological constant and radiation. The models differ from each other by the constant curvature of the spatial sections, which may be positive, negative or zero.They give rise to Wheeler-DeWitt equations for the scale factor which have the form of the Schrödinger equation for the quartic anharmonic oscillator. We find their eigenvalues and eigenfunctions by using a method first developed by Chhajlany and Malnev. After that, we use the eigenfunctions in order to construct wave packets for each case and evaluate the time-dependent expected value of the scale factors. We find for all of them that the expected values of the scale factors oscillate between maximum and minimum values. Since the expectation values of the scale factors never vanish, we conclude that these models do not have singularities.

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.

The modeling of the early universe is done through the quantization of a Friedmann-Robertson-Walker model with positive curvature. The material content consists of two fluids: radiation and Chaplygin gas. The quantization of these models is made by following the Wheeler and DeWitt's prescriptions. Using the Schutz formalism, the time notion is recovered and the Wheeler-DeWitt equation transforms into a time dependent Schrödinger equation, which rules the dynamics of the early universe, under the action of an effective potential V ef . Using a finite differences method and the Crank-Nicholson scheme, in a code implemented in the program OCTAVE, we solve the corresponding time dependent Schrödinger equation and obtain the time evolution of a initial wave packet. This wave packet satisfies appropriate boundary conditions. The calculation of the tunneling probabilities shows that the universe may emerge from the Planck era to an inflationary phase. It also shows that, the tunneling probability is a function of the mean energy of the initial wave packet and of two parameters related to the Chaplygin gas. We also show a comparison between these results and those obtained by the WKB approximation.

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 fluctuations. We solve them numerically for linear and spherical perturbations and follow the time evolution 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. Spherical perturbations are strongly damped and almost do not propagate. We study these equations also for matter at finite temperature. Finally we consider the limiting case of shock wave formation.Comment: 28 pages, 8 figure

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We study the radial expansion of cylindrical tubes in a hot QGP. These tubes are treated as perturbations in the energy density of the system which is formed in heavy ion collisions at RHIC and LHC. We start from the equations of relativistic hydrodynamics in two spatial dimensions and cylindrical symmetry and perform an expansion of these equations in a small parameter, conserving the nonlinearity of the hydrodynamical formalism. We consider both ideal and viscous fluids and the latter are studied with a relativistic Navier-Stokes equation. We use the equation of state of the MIT bag model. In the case of ideal fluids we obtain a breaking wave equation for the energy density fluctuation, which is then solved numerically. We also show that, under certain assumptions, perturbations in a relativistic viscous fluid are governed by the Burgers equation. We estimate the typical expansion time of the tubes.