On the stability of two-flavor and three-flavor quark matter in quark stars within the framework of NJL model

2020 ◽  
Vol 35 (39) ◽  
pp. 2050321 ◽  
Author(s):  
Qianyi Wang ◽  
Tong Zhao ◽  
Hongshi Zong
Keyword(s):  
Quark Matter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Quark Stars ◽  
Njl Model ◽  
The Stability ◽  
Chiral Susceptibility ◽  
Strong Interaction Matter

Following our recently proposed self-consistent mean field approximation approach, we have done some researches on the chiral phase transition of strong interaction matter within the framework of Nambu-Jona-Lasinio (NJL) model. The chiral susceptibility and equation of state (EOS) are computed in this work for both two-flavor and three-flavor quark matter for contrast. The Pauli–Villars scheme, which can preserve gauge invariance, is used in this paper. Moreover, whether the three-flavor quark matter is more stable than the two-flavor quark matter or not in quark stars is discussed in this work. In our model, when the bag constant are the same, the two-flavor quark matter has a higher pressure than the three-flavor quark matter, which is different from what Witten proposed in his pioneering work.

scholarly journals The Smoluchowski Ensemble—Statistical Mechanics of Aggregation

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1181
Author(s):  
Themis Matsoukas
Keyword(s):  
Sol Gel ◽  
Scaling Limit ◽  
Mean Field ◽  
Central Element ◽  
Field Approximation ◽  
Fixed Number ◽  
Mean Field Approximation ◽  
The Mean ◽  
Sol Gel Transition ◽  
The Stability

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

scholarly journals SU(3) Polyakov linear-sigma model: Conductivity and viscous properties of QCD matter in thermal medium

2016 ◽  
Vol 31 (34) ◽  
pp. 1650175 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
M. T. Hussein
Keyword(s):  
Lattice Qcd ◽  
Mean Field ◽  
Field Approximation ◽  
Linear Sigma Model ◽  
Dense Medium ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Strange Quarks ◽  
Transition Formula ◽  
Thermal Medium

In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-[Formula: see text] model (PLSM) is analyzed for chiral phase transition, [Formula: see text] and [Formula: see text] and for deconfinement order-parameters, [Formula: see text] and [Formula: see text] of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates [Formula: see text]. All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [Formula: see text] and heat [Formula: see text] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, [Formula: see text] and [Formula: see text], respectively, and compared them with recent lattice QCD. Predictions for [Formula: see text] and [Formula: see text] are introduced. We conclude that our results on various transport properties show some essential ingredients, that these properties likely come up with, in studying QCD matter in thermal and dense medium.

scholarly journals Hybrid Stars in the Framework of NJL Models

2017 ◽  
Vol 45 ◽  
pp. 1760026 ◽  
Author(s):  
Gustavo A. Contrera ◽  
Milva Orsaria ◽  
I. F. Ranea-Sandoval ◽  
Fridolin Weber
Keyword(s):  
Phase Transition ◽  
Quark Matter ◽  
Mean Field ◽  
Field Approximation ◽  
Hadronic Matter ◽  
High Mass ◽  
Mean Field Approximation ◽  
Soft Phase ◽  
Non Local ◽  
Hybrid Stars

We compute models for the equation of state (EoS) of the matter in the cores of hybrid stars. Hadronic matter is treated in the non-linear relativistic mean-field approximation, and quark matter is modeled by three-flavor local and non-local Nambu−Jona-Lasinio (NJL) models with repulsive vector interactions. The transition from hadronic to quark matter is constructed by considering either a soft phase transition (Gibbs construction) or a sharp phase transition (Maxwell construction). We find that high-mass neutron stars with masses up to [Formula: see text] may contain a mixed phase with hadrons and quarks in their cores, if global charge conservation is imposed via the Gibbs conditions. However, if the Maxwell conditions is considered, the appearance of a pure quark matter core either destabilizes the star immediately (commonly for non-local NJL models) or leads to a very short hybrid star branch in the mass-radius relation (generally for local NJL models).

First Principles Study of the Phase Transitions of MnAs

2006 ◽  
Vol 941 ◽  
Author(s):  
Ivan Rungger ◽  
Stefano Sanvito
Keyword(s):  
Phase Transition ◽  
Curie Temperature ◽  
Cell Volume ◽  
Order Phase Transition ◽  
Structural Changes ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
First Order Phase Transition ◽  
The Stability

ABSTRACTThe magnetic and structural properties of MnAs are investigated by mapping ab initio total energies onto a Heisenberg Hamiltonian. We study the dependence of the Curie temperature over the unit cell volume and an orthorhombic distortion by using the mean field approximation, and find that for orthorhombically distorted cells the Curie temperature is much smaller than for hexagonal cells. We provide an explanation for the structural changes of both the first order phase transition at 318 K and the second order phase transition at 400 K, with the cell volume driving the stability of the different structures in the paramagnetic state. The stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7 Å, above which it remains hexagonal.

The behaviors of the solutions of the quark gap equation in the NJL model with the self-consistent mean field approximation

2021 ◽  
Author(s):  
Zu-Qing Wu ◽  
Jia-Lun Ping ◽  
Hong-Shi Zong
Keyword(s):  
Chiral Limit ◽  
Mean Field ◽  
Stable Solution ◽  
Field Approximation ◽  
The Self ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Gap Equation ◽  
Self Consistent ◽  
Exchange Channel

In this paper, we use the self-consistent mean field approximation to study the Quantum Chromodynamics (QCD) phase transition. In the self-consistent mean field approximation of the Nambu–Jona-Lasinio (NJL) model, a parameter [Formula: see text] is introduced, which reflects the weight of “direct” channel and the “exchange” channel and needs to be determined by experiments (as mentioned in a recent work [T. Zhao, W. Zheng, F. Wang, C.-M. Li, Y. Yan, Y.-F. Huang and H.-S. Zong, Phys. Rev. D 100, 043018 (2019)], the results with [Formula: see text] are in good agreement with astronomical observation data on the latest binary neutron star merging. This indicates that the contribution of “exchange” channel should be considered, and [Formula: see text] is a possible choice). By comparing the results with different parameter [Formula: see text]’s ([Formula: see text], [Formula: see text] and [Formula: see text]), we study the influence of “exchange” channel on the behavior of the solutions of the quark gap equation and the critical point of chiral phase transition. Our results show that the second-order chiral phase turns to the crossover from the chiral limit to the non-chiral limit around [Formula: see text] in the case of [Formula: see text]. The difference of the quark mass with different [Formula: see text]’s mainly occurs in the intermediate temperatures for the different fixed chemical potentials. At zero temperature and the chemical potential [Formula: see text] there will be two solutions (including a meta-stable solution) of gap equation with [Formula: see text], and as [Formula: see text] increases it will be only one solution left (the meta-stable solution will disappear until [Formula: see text]). Besides, the discrepancy of the critical temperature (above which the pseudo-Wigner solution and negative Nambu solution will disappear) in the three cases of [Formula: see text] will become large when the chemical potential increases.

scholarly journals TIME-DEPENDENT VARIATIONAL APPROACH TO BOSE–EINSTEIN CONDENSATION

2000 ◽  
Vol 14 (01) ◽  
pp. 1-11 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Variational Approach ◽  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Collective Oscillations ◽  
The Stability ◽  
Bose Einstein

We discuss the mean-field approximation for a trapped weakly-interacting Bose–Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross–Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.

EFFICIENT DESCRIPTION FOR π AND σ MESONS BY RESONATING MEAN-FIELD APPROXIMATION TO TWO-FLAVOR NAMBU-JONA-LASINIO MODEL

2006 ◽  
Vol 15 (05) ◽  
pp. 1087-1114 ◽  
Author(s):  
SEIYA NISHIYAMA ◽  
JOÃO DA PROVIDÊNCIA ◽  
OSAMU OHNO
Keyword(s):  
Order Parameter ◽  
Degrees Of Freedom ◽  
Decay Constant ◽  
Mean Field ◽  
Mass Term ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pion Decay ◽  
Pion Decay Constant ◽  
Njl Model

We have applied the resonating (Res-) mean-field approximation (MFA) to fermion systems with large quantum fluctuations over the usual MFA to a naive Nambu-Jona-Lasinio (NJL) model involving no current quark mass term. In our approach, as part of the model the normalization volume is kept finite, which plays an important role. This attempt has been quite successful in explaining the pion and sigma-meson masses, but the values of the order parameter for quark condensate and the pion decay constant are too small. This fact suggests us that the Res-MFA including no isospin causes such a problem. To avoid the serious drawback, if we naturally extend the NJL model to include two-flavor degrees of freedom and make an SU(2)f resonating Hartree-Fock (Res-HF) approximation, it is expected that the magnitudes of the order parameter and the pion decay constant are much improved. Using this extended NJL model, they are calculated again and both the numerical values [Formula: see text] and fπ reach good agreements with their experimental ones.

scholarly journals Revisiting quark stars under the influence of strong magnetic fields

2012 ◽  
Vol 8 (S291) ◽  
pp. 458-458
Author(s):  
Debora Menezes
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Quark Matter ◽  
Mean Field ◽  
Heavy Ion ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Solar Mass ◽  
Strong Magnetic Fields ◽  
The Masses

AbstractQuark matter at finite temperature and subject to strong magnetic fields is possibly present in the early stages of heavy ion collisions and in the interior of protoneutron stars. We use the mean field approximation to investigate this type of quark matter described by the Nambu–Jona-Lasinio model. The energy per baryon of magnetized quark matter becomes more bound than nuclear matter made of iron nuclei, for magnetic fields around 1019 G. When the su(3) NJL model is applied to stellar matter, the maximum mass configurations are always above 1.45 solar masses and may be as high as 1.9 solar masses for a central magnetic field of 1018 G. These numbers are within the masses of observed neutron stars but exclude the recently measured star with 1.97 solar mass.The effect of the magnetic field on the effective quark masses and chemical potentials is only felt for quite strong magnetic fields, above 5 × 1018 G, with larger effects for the lower densities. Spin polarizations are more sensitive to weaker magnetic fields and are larger for lower temperatures and lower densities.

scholarly journals Susceptibilities and critical exponents within the Nambu–Jona-Lasinio model

2015 ◽  
Vol 30 (34) ◽  
pp. 1550199 ◽  
Author(s):  
Yi-Lun Du ◽  
Ya Lu ◽  
Shu-Sheng Xu ◽  
Zhu-Fang Cui ◽  
Chao Shi ◽  
...  
Keyword(s):  
Critical Exponents ◽  
Chemical Potential ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Coupled Equations ◽  
Theoretical Predictions ◽  
The Mean ◽  
Chiral Susceptibility ◽  
Quark Number Susceptibility

In the mean field approximation of (2 + 1)-flavor Nambu–Jona-Lasinio model, we strictly derive several sets of coupled equations for the chiral susceptibility, the quark number susceptibility, etc. at finite temperature and quark chemical potential. The critical exponents of these susceptibilities in the vicinity of the QCD critical end point (CEP) are presented in SU(2) and SU(3) cases, respectively. It is found that these various susceptibilities share almost the same critical behavior near the CEP. The comparisons between the critical exponents for the order parameters and the theoretical predictions are also included.

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