We present a non-extensive version of the Polyakov-Nambu-Jona-Lasinio model which is based on the non-extentive statistical mechanics. This new statistics is characterized by a dimensionless non-extensivity parameter $q$ that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs statistics (when $q\rightarrow1$, it returns to the Boltzmann-Gibbs case). Using this q-Polyakov-Nambu-Jona-Lasinio model and including two different Polyakov-loop potentials, we discussed the influence of the parameter $q$ on chiral and deconfinement phase transition, various thermodynamic quantities and transport coefficients at finite temperature and zero quark chemical potential. We found that the Stefan-Boltzmann limit is actually related to the choice of statistics. For example, in the Tsallis statistics, the thermodynamic quantities $\fracε{T^{4}}$, $\frac{p}{T^{4}}$ and $\frac{s}{T^{3}}$ all increase with $q$, exceed their usual Stefan-Boltzmann limits and tend to a new $q$-related Tsallis limit at temperature high enough. Interestingly, however, due to a surprising cancellation, the high temperature limit of $c_{s}^{2}$ is still its SB limit $1/3$. In addition, we found some similarities between the non-extensive effect and the finite-size effect. For example, as $q$ increases (size decreases), the criticality of $\frac{c_{v}}{T^{3}}$ and $c_{s}^{2}$ gradually disappears. Besides, in order to better study the non-extensive effect, we defined a new susceptibility and calculated the response of thermodynamic quantities and transport coefficients to $q$. And found that their response patterns are different.
We study the chiral phase transition of the two flavor Nambu-Jona-Lasinio (NJL) model in a sphere with the MIT boundary condition. We find that the MIT boundary condition results in much stronger finite size effects than the antiperiodic boundary condition. Our work may be helpful to study the finite size effects in heavy-ion collision in a more realistic way.
We present an analysis of two-current correlations for the pion in the Nambu--Jona-Lasinio model, with Pauli--Villars regularization. We provide explicit expressions in momentum space for two-current correlations corresponding to the zeroth component of the vector Dirac bilinear in the quark vertices, which has been evaluated on the lattice. The numerical results show a remarkable qualitative agreement with recent lattice data. The factorization approximation into one-body currents is discussed.
In this review, we summarize recent progress on the possible phases of quantum chromodynamics (QCD) in the presence of a strong magnetic field, mainly from the views of the chiral effective Nambu--Jona-Lasinio model. Four kinds of phase transitions are explored in detail: chiral symmetry breaking and restoration, neutral pseudoscalar superfluidity, charged pion superfluidity and charged rho superconductivity. In particular, we revisit the unsolved problems of inverse magnetic catalysis effect and competition between the chiral density wave and solitonic modulation phases. It is shown that usef…
We have investigated shear viscosity of quark matter in presence of a strong uniform magnetic field background where Nambu-Jona-Lasinio model has been considered to describe the magneto-thermodynamical properties of the medium. In presence of magnetic field, shear viscosity coefficient gets split into different components because of anisotropy in tangential stress of the fluid. Four different components can be merged to two components in limit of strong field, where collisional width of quark becomes much lower than its synchrotron frequency. A simplified contact diagram of quark-quark interac…
In this work we study the electrized quark matter under finite temperature and density conditions in the context of the SU(2) and SU(3) Nambu--Jona-Lasinio models. To this end, we evaluate the effective quark masses and the Schwinger quark-antiquark pair production rate. For the SU(3) NJL model we incorporate in the Lagrangian the 't Hooft determinant and we present a set of analytical expressions more convenient for numerical evaluations. We predict a decrease of the pseudocritical electric field with the increase of the temperature for both models and a more prominent production rate for the…
Deconfinement and chiral restoration within the SU(3) Polyakov--Nambu--Jona-Lasinio and entangled Polyakov--Nambu--Jona-Lasinio models in an external magnetic field
