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We show that the pseudogap of the quark density of states is formed in hot quark matter as a precursory phenomenon of the color superconductivity on the basis of a low-energy effective theory. We clarify that the decaying process of quarks near Fermi surface to a hole and the diquark soft mode (qq)_{soft} is responsible for the formation of the pseudogap. Our result suggests that the pseudogap is a universal phenomenon in strong coupling superconductors.
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We show how the quasiparticle picture of quarks changes near but above the critical temperature T_c of the color-superconducting phase transition in the heated quark matter. We demonstrate that a non-Fermi liquid behavior of the matter develops drastically when the diquark coupling constant is increased owing to the coupling of the quark with the pairing soft mode: We clarify that the depression and eventually the appearance of a gap structure in the spectral function as well as the anomalous quark dispersion relation of the quark can be understood in terms of the resonant scattering between the incident quark and a particle near the Fermi surface to make the pairing soft mode.
We apply Ginzburg-Landau theory to determine BCS pairing in a strongly-coupled uniform superfluid of three-flavor massless quarks in flavor equilibrium. We elucidate the phase diagram near the critical temperature in the space of the parameters characterizing the thermodynamic potential terms of fourth order in the pairing gap. Within the color and flavor antisymmetric channel with zero total angular momentum, the phase diagram contains an isoscalar (IS) color-antitriplet phase and a color-flavor-locked (CFL) phase, reached by a second order transition from the normal state, as well as states reached by a first order transition. We complement the general Ginzburg-Landau approach by deriving the high-density asymptotic form of the Ginzburg-Landau free energy from the weak-coupling gap equation. The dynamically-screened, long-range color magnetic interactions are taken into account in solving the gap equation. We find that in the limit of weak coupling, the IS phase is less favorable near the transition temperature than the CFL phase. In view of the fact that deconfined quark matter must be color charge neutral, we incorporate the constraint of overall color neutrality into the Ginzburg-Landau theory and the gap equation. This constraint yields a disparity in the chemical potential between colors and reduces the size of the gap, in the presence of the anisotropy of the order parameters in color space. In comparison with the case in which there are no chemical potential differences between colors and hence the superfluid generally has nonzero net color charge, we find that while the constraint of color neutrality has only negligible effects on the gap in the weak coupling regime, it appreciably destabilizes the IS phase in the strong coupling regime without affecting the CFL phase.
We study a model for color superconductivity with both three colors and massless flavors including quark pairing. By using the Hamiltonian in the color-flavor basis we can calculate the quantum entropy. From this we are able to further investigate the phases of the color superconductor, for which we find a rather sharp transition to color superconductivity above a chemical potential around $290 $MeV.
A coexistent phase of spin polarization and color superconductivity in high-density QCD is investigated using a self-consistent mean-field method at zero temperature. The axial-vector current stemming from the Fock exchange term of the one-gluon-exchange interaction has a central role to cause spin polarization. The magnitude of spin polarization is determined by the coupled Schwinger-Dyson equation with a superconducting gap function. As a significant feature the Fermi surface is deformed by the axial-vector self-energy and then rotational symmetry is spontaneously broken. The gap function is also taken to be anisotropic in accordance with the deformation. As a result of numerical calculation, it is found that spin polarization barely conflicts with color superconductivity, but almost coexists with it.
The thermal evolution of isothermal neutron stars is studied with matter both in the hadronic phase as well as in the mixed phase of hadronic matter and strange quark matter. In our models, the dominant early-stage cooling process is neutrino emission via the direct Urca process. As a consequence, the cooling curves fall too fast compared to observations. However, when superfluidity is included, the cooling of the neutron stars is significantly slowed down. Furthermore, we find that the cooling curves are not very sensitive to the precise details of the mixing between the hadronic phase and the quark phase and also of the pairing that leads to superfluidity.
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