Relativistic dissipative hydrodynamics with spontaneous symmetry breaking

In this paper we consider dissipative hydrodynamic equations for systems with continuous broken symmetries. We first present the case of superfluidity, in which the symmetry U(1) is broken and then generalize to the chiral symmetry $SU(2)_L \times SU(2)_R$. The corresponding new transport coefficients are introduced.Comment: 5 pages, RevTeX Minor changes, version accepted for publicatio

A consistent approximation scheme beyond RPA for bosons

In this paper, we develop a consistent extension of RPA for bosonic systems. In order to illustrate the method, we consider the case of the anharmonic oscillator. We compare our results with those obtained in mean-field and standard RPA approaches, with the exact ones and show that they are very close to the exact ones.Comment: 19 pages, Latex, 1 figure, accepted version in EPJ

Hydrodynamics with spontaneous symmetry breaking: application to relativistic heavy ion collisions

In this paper we apply hydrodynamics for systems with continuous broken symmetries to heavy ion collisions in the framework of (1+1) dimensional Bjorken model. The temperature profile with respect to proper time determined in that context exhibits no differences with the ideal fluid. On the contrary, it is shown that the profile obtained when M\"{u}ller-Israel-Stewart second order theory of dissipation is included on top of standard hydrodynamics indicates a slower cooling of the system.Comment: 5 pages, 2 figures, version accepted for publication as a Brief Report in Physical Review

Extended Skyrme Equation of State in asymmetric nuclear matter

We present a new equation of state for infinite systems (symmetric, asymmetric and neutron matter) based on an extended Skyrme functional constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces with very good accuracy the main features of microscopic calculations and it is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest

Spurious finite-size instabilities in nuclear energy density functionals: spin channel

It has been recently shown, that some Skyrme functionals can lead to non-converging results in the calculation of some properties of atomic nuclei. A previous study has pointed out a possible link between these convergence problems and the appearance of finite-size instabilities in symmetric nuclear matter (SNM) around saturation density. We show that the finite-size instabilities not only affect the ground state properties of atomic nuclei, but they can also influence the calculations of vibrational excited states in finite nuclei. We perform systematic fully-self consistent Random Phase Approximation (RPA) calculations in spherical doubly-magic nuclei. We employ several Skyrme functionals and vary the isoscalar and isovector coupling constants of the time-odd term $\mathbf{s}\cdot \Delta \mathbf{s}$ . We determine critical values of these coupling constants beyond which the RPA calculations do not converge because RPA the stability matrix becomes non-positive.By comparing the RPA calculations of atomic nuclei with those performed for SNM we establish a correspondence between the critical densities in the infinite system and the critical coupling constants for which the RPA calculations do not converge. We find a quantitative stability criterion to detect finite-size instabilities related to the spin $\mathbf{s}\cdot \Delta \mathbf{s}$ term of a functional. This criterion could be easily implemented into the standard fitting protocols to fix the coupling constants of the Skyrme functional

Collective modes of trapped Fermi gases with in-medium interaction

Due to Pauli blocking of intermediate states, the scattering matrix (or $T$ matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium $T$ matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.Comment: 17 page

Random Phase Approximation and Extensions Applied to a Bosonic Field Theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $\phi^4$ theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.Comment: 30 pages, LaTeX file, 10 figures included, final version accepted in EPJ

Linear response in infinite nuclear matter as a tool to reveal finite size instabilities

Nuclear effective interactions are often modelled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd-even or rotating nuclei. In this article, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.Comment: Based on talk presented at 18th Nuclear Physics Workshop "Maria and Pierre Curie", 2011, Kazimierz, Polan

How to preserve symmetries with cut-off regularized integrals?

We present a prescription to calculate the quadratic and logarithmic divergent parts of several integrals employing a cutoff in a coherent way, i.e. in total agreement with symmetry requirements. As examples we consider one-loop Ward identities for QED and a phenomenological chiral model.Comment: 11 pages, 3 graph

Fitting Skyrme functionals using linear response theory

Recently, it has been recently shown that the linear response theory in symmetric nuclear matter can be used as a tool to detect finite size instabilities for different Skyrme functionals. In particular it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this article we present a new fitting protocol that uses this correlation to add new additional constraint in Symmetric Infinite Nuclear Matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameters set for a new Skyrme functional which includes central and spin-orbit parts and which is free from instabilities by construction.Comment: Proceeding of 19th Nuclear Physics Workshop "Marie & Pierre Curie" Kazimierz 201