D. A. Fogaça

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.

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.

The quark gluon plasma equation of state and the expansion of the early Universe

Abstract Our knowledge of the equation of state of the quark gluon plasma has been continuously growing due to the experimental results from heavy ion collisions, due to recent astrophysical measurements and also due to the advances in lattice QCD calculations. The new findings about this state may have consequences on the time evolution of the early Universe, which can be estimated by solving the Friedmann equations. The solutions of these equations give the time evolution of the energy density and also of the temperature in the beginning of the Universe. In this work we compute the time evolution of the QGP in the early Universe, comparing several equations of state, some of them based on the MIT bag model (and on its variants) and some of them based on lattice QCD calculations. Among other things, we investigate the effects of a finite baryon chemical potential in the evolution of the early Universe.

Bubble dynamics and the quark-hadron phase transition in nuclear collisions

We study the nucleation of a quark gluon plasma (QGP) phase in a hadron gas at low temperatures and high baryon densities. This kind of process will presumably happen very often in nuclear collisions at FAIR and NICA. When the appropriate energy densities (or baryon densities) and temperatures are reached the conversion of one phase into another is not instantaneous. It is a complex process, which involves the nucleation of bubbles of the new phase. One important element of this transition process is the rate of growth of a QGP bubble. In order to estimate it we solve the Relativistic Rayleigh

Compact stars with strongly coupled quark matter in a strong magnetic field

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Self-bound interacting QCD matter in compact stars

Plesset equation which governs the dynamics of a relativistic spherical bubble in a strongly interacting medium. The baryon rich hadron gas is represented by the nonlinear Walecka model and the QGP is described by the MIT bag model and also by a mean field model of QCD.

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

Some time ago we have derived from the QCD Lagrangian an equation of state (EOS) for the cold quark matter, which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to non-perturbative effects. Later we applied this EOS to the study of compact stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. We found maximum masses of the sequences with more than two solar masses, in agreement with the recent experimental observations. In the present work we include the magnetic field in the equation of state and study how it changes the stability conditions and the mass-radius curves.

Nonlinear waves in second order conformal hydrodynamics

The quark gluon plasma (QGP) at zero temperature and high baryon number is a system that may be present inside compact stars. It is quite possible that this cold QGP shares some relevant features with the hot QGP observed in heavy ion collisions, being also a strongly interacting system. In a previous work we have derived from the QCD Lagrangian an equation of state (EOS) for the cold QGP, which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to non-perturbative effects. Here we apply this EOS to the study of neutron stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. The maximum masses of the sequences exceed two solar masses, in agreement with the recently measured values of the mass of the pulsar PSR J1614-2230, and the corresponding radii around 10-11 km.

On the radial expansion of tubular structures in a 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.

Waves in magnetized quark matter

Abstract In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel–Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a “soliton-like” wave solution in Israel–Stewart hydrodynamics despite the presence of dissipation and relaxation effects.