Narrow Results

We investigate the sound absorption in quark matter due to the interaction of the sound wave with the precritical fluctuations of the diquark-pair field above $T_{\mathrm{\text{c}}}$. The soft collective mode of the pair field is derived using the time-dependent Ginzburg–Landau functional with random Langevin forces. The strong absorption near the phase transition line may be viewed as a manifestation of Mandelshtam–Leontovich slow relaxation time theory.

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R¹ × S¹ space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μ_I, μ. The consideration is performed in the large N_c limit, where N_c is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S¹) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μ_I and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

Two-loop corrections for the standard Abelian Nambu–Jona-Lasinio model are obtained with the optimized perturbation theory (OPT) method. These contributions improve the usual mean-field and Hartree–Fock results by generating a 1/N_c suppressed term, which only contributes at finite chemical potential. We take the zero temperature limit observing that, within the OPT, chiral symmetry is restored at a higher chemical potential μ, while the resulting equation of state is stiffer than the one obtained when mean-field is applied to the standard version of the model. In order to understand the physical nature of these finite N_c contributions, we perform a numerical analysis to show that the OPT quantum corrections mimic effective repulsive vector–vector interaction contributions. We also derive a simple analytical approximation for the mass gap, accurate at the percent level, matching the mean-field approximation extended by an extra vector channel to OPT. For μ ≳ μ_c the effective vector coupling matching OPT is numerically close (for the Abelian model) to the Fierz-induced Hartree–Fock value G/(2N_c), where G is the scalar coupling, and then increases with μ in a well-determined manner.