Fermi-liquid properties of nuclear matter in a relativistic mean-field theory

The Fermi-liquid properties of the model nuclear system described by a relativistic quantum field theory are examined in terms of a relativistic extension of Landau's Fermi-liquid theory. The relativistic Landau parameters are derived microscopically from the ground state energy in the mean-field approximation, and are used to describe the thermodynamic properties of the system, such as the compressibility, the symmetry energy and the hydrodynamic sound velocities. We reproduce the previous results at nuclear saturation density (n₀ = 0.19 fm⁻³) and extrapolate to all density regions. It is shown that the system exhibits instability against the long wavelength density fluctuations in the low density region (n_B <0.70 n₀) and becomes stable at and above the nuclear saturation density due to the relativistic reduction of the attractive scalar meson component in the quasiparticle interaction. In the extreme high-density region, we reproduce the correct causal results for sound velocities. The existence of collisionless zero-sound oscillation is also examined.     

Center-symmetric effective theory for two-color quark matter

We revisit the center-symmetric dimensionally reduced effective theory for two-color Yang-Mills theory at high temperature. This effective theory includes an order parameter for deconfinement and thus allows to broaden the range of validity of the conventional three-dimensional effective theory (EQCD) towards the confining phase transition. We extend the previous results by including the effects of massive quarks with nonzero baryon chemical potential. The parameter space of the theory is constrained by leading-order matching to the Polyakov loop effective potential of two-color QCD. Once all the parameters are fixed, the effective theory can provide model-independent predictions for the physics above the deconfinement transition, thus bridging the gap between large-scale numerical simulations and semi-analytical calculations within phenomenological models.     

Dense nuclear matter: Landau Fermi-liquid theory and chiral Lagrangian with scaling

The relation between the effective chiral Lagrangian whose parameters scale according to Brown and Rho scaling (“BR scaling”) and Landau Fermi-liquid theory for hadronic matter is discussed in order to make a basis to describe the fluctuations under the extreme condition relevant to neutron stars. It is suggested that BR scaling gives the background around which the fluctuations are weak. A simple model with BR-scaled parameters is constructed and reproduces the properties of the nuclear ground state at normal nuclear matter density successfully. It shows that the tree level in the model Lagrangian is enough to describe the fluctuations around BR-scaled background. The model Lagrangian is consistent thermodynamically and reproduces relativistic Landau Fermi-liquid properties. Such points are important for dealing with hadronic matter under extreme condition. On the other hand, it is shown that the vector current obtained from the chiral Lagrangian is the same as that obtained from Landau–Migdal approach. We can determine the Landau parameter in terms of BR-scaled parameter. However, these two approaches provide different results, when applied to the axial charge. The numerical difference is small. It shows that the axial response is not included properly in the Landau–Migdal approach.     

Magnetic catalysis of stability of quark matter in the Nambu-Jona-Lasinio model

The effect of an external magnetic field H on the stability of quark matter is studied on the basis of the Nambu-Jona-Lasinio model. It is shown that, at H = 0, droplets of quark matter are stable only in the case where the coupling constant G is greater than some value G_bag. If H ≠ 0, stable multiquark formations may exist even for G ≤ G_bag (magnetic catalysis of stability). For G > G_bag, a magnetic field facilitates the formation of stable quark matter.     

Superconducting quark matter

In asymptotically dense quark matter, colored glue forces cause an unusual variant of superconductivity. Instead of pairing, the quarks clump in groups of six. We investigate the gap equation in the weak coupling limit, and find the leading behavior of the energy gap and the critical temperature as functions of the renormalized coupling constant.     

Faces of quark matter

Based on an analysis in the framework of a coalescence hadronization model (ALCOR) we conclude that in heavy ion collisions at CERN SPS and RHIC energies a new type of matter, the massive quark-antiquark matter is produced.     

Two-flavor quark matter in the perturbation theory with full thermodynamic consistency

Direct extrapolation of the strong interaction between quarks in pure perturbative calculation has a problem of thermodynamic inconsistency.A new term determined by thermodynamic consistency requirement could resolve it.This new term plays an important role at lower density in describing the equation of state of quark matter,while it is negligible at high density.Accordingly,the density behavior of the sound velocity becomes more reasonable,and the maximum mass of quark stars can be as large as two times the solar mass.     

Gapless color-flavor-locked quark matter

In neutral cold quark matter that is so dense that the strange quark mass Ms is unimportant, all three quark flavors pair in a color-flavor locked (CFL) pattern, and all nine fermionic quasiparticles have a gap Delta (or 2Delta). We argue that, as the density decreases (or Ms increases), there is a quantum phase transition (at M(2s/mu approximately 2Delta) to a new "gapless CFL phase" in which only seven quasiparticles have a gap. There is still an unbroken U(1)(Q) gluon/photon, but, unlike CFL, gapless CFL is a Q conductor with gapless (charged) quasiquarks and a nonzero electron density at zero temperature, so its low energy effective theory and astrophysical properties are qualitatively new. At the transition, the dispersion relations of both gapless quasiparticles are quadratic, but for larger M2s/mu, one becomes conventionally linear while the other remains quadratic, up to tiny corrections.     

Superconductivity in quark matter

Superconductivity due to the pairing of relativistic quarks in ultra-dense matter is discussed. Ginzburg-Landau equations are derived, and the possibility of an Abrikosov vortex phase is considered.     

Strange quark matter with dynamically generated quark masses

Bulk properties of strange quark matter (SQM) are investigated within the SU(3) Nambu–Jona-Lasinio model. In the chiral limit the model behaves very similarly to the MIT bag model which is often used to describe SQM. However, when we introduce realistic current quark masses, the strange quark becomes strongly disfavored, because of its large dynamical mass. We conclude that SQM is not absolutely stable.     

Quark-clustering in cold quark matter

Quarks are proposed to be grouped together to make quark-clusters due to the strong interaction in cold quark matter at a few nuclear densities,because a weakly coupling treatment of the interaction between quarks there would be inadequate.Cold quark matter is then conjectured to be in solid state （i.e.,forming a crystal structure） if the inter-cluster potential is deep enough to localize clusters in lattice.Such a solid state of cold quark matter would be very necessary for us to understand different manifestations of pulsar-like compact stars,and could not be ruled by first principles.     

Superfluidity in ultra-relativistic quark matter

Possible forms of superfluid order parameter are discussed for quark matter at densities where the Fermi energy is much greater than the mass of the quarks. Ginzburg-Landau equations for the order parameter are derived and solved.     

Color superconductivity in quark matter

Selected problems related to color superconductivity are discussed in a rather elementary way. The text was submitted by the author in English.     

Supercurrents in color-superconducting quark matter

We review the basic properties of the currCFL-K⁰ phase in dense quark matter. At asymptotically large densities, three-flavor quark matter is in the color-flavor locked (CFL) state. The currCFL-K⁰ state is a way to respond to “stress” on the quark Cooper pairing, imposed at more moderate densities by the strange quark mass and the conditions of electric and color neutrality. We show how a kaon supercurrent is incorporated in a purely fermionic formalism, and show that the net current vanishes due to cancellation of fermion and charge-conjugate fermion contributions.     

Quark-clustering in cold quark matter

Quarks are proposed to be grouped together to make quark-clusters due to the strong interaction in cold quark matter at a few nuclear densities, because a weakly coupling treatment of the interaction between quarks there would be inadequate. Cold quark matter is then conjectured to be in solid state (i.e., forming a crystal structure) if the inter-cluster potential is deep enough to localize clusters in lattice. Such a solid state of cold quark matter would be very necessary for us to understand different manifestations of pulsar-like compact stars, and could not be ruled by first principles.