G. F. Burgio

Quark matter in neutron stars within the Nambu-Jona-Lasinio model and confinement

The quark matter equation of state (EoS) derived from the standard Nambu-Jona-Lasinio (NJL) model is soft enough to render neutron stars (NS) unstable at the onset of the deconfined phase, and no pure quark matter can be actually present in its interior. Since this is a peculiarity of the NJL model, we have studied a modified NJL model with a momentum cutoff which depends on the density. This procedure, which improves the agreement between QCD and NJL model at large density, modifies the standard NJL equation of state, and then it is potentially relevant for the stability analysis of neutron stars. We show that also within this approach, the NS instability still persists, and that the vacuum pressure, as a signal of quark confinement, has a fundamental role for the NS stability. In this respect, our conclusions point to a relationship between confinement and NS stability.

Non-linear mean field dynamics in the nuclear spinodal zone

Abstract We discuss numerical simulations of mean field dynamics which strongly indicate a chaotic behavior of nuclear matter inside the spinodal region. Spontaneous symmetry-breaking — no explicit fluctuating term is considered — occurs leading to large and unpredictable density fluctuations. A proper recipe to calculate an average Lyapunov exponent in this multidimensional phase space is introduced. The latter is calculated for different values of the density in order to characterize in a quantitative way the chaotic and regular regions. These results strongly suggest that nuclear multifragmentation occurring at intermediate energy in heavy-ion reactions could be generated by a chaotic mechanism.

Dynamics of fragment formation in the nuclear spinodal region

The Vlasov-Nordheim equation is solved numerically on a lattice for nuclear matter in two dimensions. We discuss the reliability of the model at normal density and then study the response of the system to small perturbations. We find deterministic chaos inside the spinodal zone where fragment formation occurs. We discuss in detail the dynamical features of this phenomenon in order to clarify the mechanisms leading to nuclear disassembly in heavy-ion collisions.

Astrophysical constraints on the confining models : the Field Correlator Method

We explore the relevance of confinement in quark matter models for the possible quark core of neutron stars. For the quark phase, we adopt the equation of state derived with the field correlator method, extended to the zero temperature limit. For the hadronic phase, we use the microscopic Brueckner-Hartree- Fock many-body theory. We find that the currently adopted value of the gluon condensate G{sub 2}{approx_equal}0.006-0.007 GeV{sup 4}, which gives a critical temperature T{sub c}{approx_equal}170 MeV, produces maximum masses which are only marginally consistent with the observational limit, while larger masses are possible if the gluon condensate is increased.

Quark matter in Neutron Stars within the Field Correlator Method

INFN Sezione di Catania, Via Santa Sofia 64, I-95123 Catania, Italia(Dated: October 17, 2013)We discuss the appearance of quark matter in neutron star cores, focussing on the possibility thatthe recent observation of a very heavy neutron star could constrain free parameters of quark mattermodels. For that, we use the equation of state derived with the Field Correlator Method, extendedto the zero temperature limit, whereas for the hadronic phase we use the equation of state obtainedwithin both the non-relativistic and the relativistic Brueckner-Hartree-Fock many-body theory. Wefind a strong dependence of the maximum mass both on the value of the q¯q interaction V

Chaoticity in vibrating nuclear billiards.

We study the motion of classical particles confined in a two-dimensional nuclear billiard whose walls undergo periodic shape oscillations according to a fixed multipolarity. The presence of a coupling term in the single particle Hamiltonian between the particle motion and the collective coordinate generates a fully selfconsistent dynamics. We consider in particular monopole oscillations and demonstrate that self-consistency is essential in order to induce chaotic single-particle motion. We also discuss the dissipative behaviour of the wall motion and its relation with the order-to-chaos transition in the dynamics of the microscopic degrees of freedom. Analogous considerations can be extended to higher multipolarities.

Chaos vs. linear instability in the Vlasov equation: a fractal analysis characterization

In this paper we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behavior which follows an initial regular evolution is characterized through the calculation of the fractal dimension of the distribution of the final modes excited. The ambiguous role of the largest Lyapunov exponent for unstable systems is also critically reviewed. This investigation seems to confirm the crucial role played by deterministic chaos in nuclear multifragmentation. {copyright} {ital 1996 The American Physical Society.}

Generalized entropy and temperature in nuclear multifragmentation

In the framework of a 2D Vlasov model, we study the time evolution of the coarse-grained Generalized Entropy (GE) in a nuclear system which undergoes a multifragmentation (MF) phase transition. We investigate the GE both for the gas and the fragments (surface and bulk part respectively). We find that the formation of the surface causes the growth of the GE during the process of fragmentation. This quantity then characterizes the MF and confirms the crucial role of deterministic chaos in filling the new available phase-space: at variance with the exact time evolution, no entropy change is found when the linear response is applied. Numerical simulations were used also to extract information about final temperatures of the fragments. From a fitting of the momentum distribution with a Fermi-Dirac function we extract the temperature of the fragments at the end of the process. We calculate also the gas temperature by averaging over the available phase space. The latter is a few times larger than the former, indicating a gas not in equilibrium. Though the model is very schematic, this fact seems to be very general and could explain the discrepancy found in experimental data when using the slope of light particles spectra instead of the double ratio of isotope yields method in order to extract the nuclear caloric curve.

Beyond liear response theory in multifragmentation

Abstract Within the framework of the Vlasov equation, we discuss the validity of linear response theory in the dynamics of fragment formation. Considering a hot piece of nuclear matter inside the spinodal zone, we demonstrate by numerical simulations that after the first stages of the time evolution, nonlinear terms become important and cannot be neglected. Nonlinear and chaotic dynamics seems to characterize multifragmentation occurring in heavy-ion collisions.

Neutron Star masses from the Field Correlator Method Equation of State

We analyse the hadron-quark phase transition in neutron stars by confronting the hadronic Equation of State (EoS) obtained according to the microscopic Brueckner- Hartree-Fock many body theory, with the quark matter EoS derived within the Field Cor- relator Method. In particular, the latter EoS is only parametrized in terms of the gluon condensate and the large distance quark-antiquark potential, so that the comparison of the results of this analysis with the most recent measurements of heavy neutron star masses provides some physical constraints on these two parameters.