Cooper pairing and finite-size effects in a NJL-type four-fermion model

Starting from a NJL-type model with N fermion species fermion and difermion condensates and their associated phase structures are considered at nonzero chemical potential $\mu$ and zero temperature in spaces with nontrivial topology of the form $S^1\otimes S^1\otimes S^1$ and $R^2\otimes S^1$. Special attention is devoted to the generation of the superconducting phase. In particular, for the cases of antiperiodic and periodic boundary conditions we have found that the critical curve of the phase transitions between the chiral symmetry breaking and superconducting phases as well as the corresponding condensates and particle densities strongly oscillate vs $\lambda\sim 1/L$, where $L$ is the length of the circumference $S^1$. Moreover, it is shown that at some finite values of $L$ the superconducting phase transition is shifted to smaller values both of $\mu$ and particle density in comparison with the case of $L=\infty$.Comment: 13 pages, 13 figures; minor changes; new references added; version accepted to PR

Mesons and diquarks in the color neutral 2SC phase of dense cold quark matter

The spectrum of meson and diquark excitations of dense color neutral cold quark matter is investigated in the framework of a 2-flavored Nambu--Jona-Lasinio type model, including a quark $\mu$- and color $\mu_8$ chemical potential. It was found out that in the color superconducting (2SC) phase, i.e. at $\mu>\mu_c=342$ MeV, $\mu_8$ aquires rather small values $\sim$ 10 MeV in order to ensure the color neutrality. In this phase the $\pi$- and $\sigma$ meson masses are evaluated around $\sim$ 330 MeV. The spectrum of scalar diquarks in the color neutral 2SC phase consists of a heavy ($\rm SU_c(2)$-singlet) resonance with mass $\sim$ 1100 MeV, four light diquarks with mass $3|\mu_8|$, and one Nambu --Goldstone boson which is in accordance with the Goldstone theorem. Moreover, in the 2SC phase there are five light stable particles as well as a heavy resonance in the spectrum of pseudo-scalar diquarks. In the color symmetric phase, i.e. for $\mu <\mu_c$, a mass splitting of scalar diquarks and antidiquarks is shown to arise if $\mu\ne 0$, contrary to the case of $\mu = 0$, where the masses of scalar antidiquarks and diquarks are degenerate at the value $\sim$~700 MeV. If the coupling strength in the pseudo-scalar diquark channel is the same as in the scalar diquark one (as for QCD-inspired NJL models), then in the color symmetric phase pseudo-scalar diquarks are not allowed to exist as stable particles.Comment: 18 pages, 4 figures; version accepted for the publication in PR

Finite size effects in the Gross-Neveu model with isospin chemical potential

The properties of the two-flavored Gross-Neveu model in the (1+1)-dimensional $R^1\times S^1$ spacetime with compactified space coordinate are investigated in the presence of the isospin chemical potential $\mu_I$. The consideration is performed in the limit $N_c\to\infty$, i.e. in the case with infinite number of colored quarks. It is shown that at $L=\infty$ ($L$ is the length of the circumference $S^1$) the pion condensation phase is realized for arbitrary small nonzero $\mu_I$. At finite values of $L$, the phase portraits of the model in terms of parameters $\nu\sim\mu_I$ and $\lambda\sim 1/L$ are obtained both for periodic and antiperiodic boundary conditions of the quark field. It turns out that in the plane $(\lambda,\nu)$ there is a strip $0\le\lambda<\lambda_c$ which lies as a whole inside the pion condensed phase. In this phase the pion condensation gap is an oscillating function vs both $\lambda$ (at fixed $\nu$) and $\nu$ (at fixed $\lambda$).Comment: 12 pages, 8 figures; one reference added; accepted for publication in PR

Chiral phase transitions in strong chromomagnetic fields at finite temperature and dimensional reduction

Dynamical fermion mass generation in external chromomagnetic fields is considered at non--zero temperature. The general features of dynamical chiral symmetry breaking ($D\chi SB$) are investigated for several field configurations in relation to their symmetry properties and the form of the quark spectrum. According to the fields, there arises dimensional reduction by one or two units. In all cases there exists $D\chi SB$ even at weak quark attraction, confirming the idea about the dimensional insensitivity of this mechanism in a chromomagnetic field.Comment: LATEX file, 12 pages, no figure

Mesons and diquarks in neutral color superconducting quark matter with β\beta-equilibrium

The spectrum of meson and diquark excitations in cold color-superconducting (2SC) quark matter is investigated under local color and electric neutrality constraints with $\beta$-equilibrium. A 2-flavored Nambu--Jona-Lasinio type model including a baryon $\mu_B$, color $\mu_8$, and electric $\mu_Q$ chemical potentials is used. Two relations between coupling constants $H$ and $G$ in the diquark- and quark-antiquark channels, correspondingly, are treated, $H=3G/4$ and $H=G$. At $H=3G/4$ the gapless- and at $H=G$ the gapped neutral color superconductivity is realized. It is shown that color and electrical neutrality together with $\beta$-equilibrium lead to a strong mass splitting within the pion isotriplet in the 2SC phase (both gapped and gapless), in contrast with non--neutral matter. It is also shown that the properties of the physical $SU(2)_c$-singlet diquark excitation in the 2SC ground state varies for different parameterization schemes. Thus, for $H=3G/4$ one finds a heavy resonance with mass $\sim$ 1100 MeV in the non--neutral (gapped) case, whereas, if neutrality is imposed, a stable diquark with mass $\sim\mu_Q\sim$ 200 MeV appears in the gapless 2SC phase. For $H=G$, there is again a resonance (with the mass $\sim$ 300 MeV) in the neutral gapped 2SC phase. Hence, the existence of the stable massive SU(2)$_c$-singlet diquark excitation is a new peculiarity of the gapless 2SC.Comment: 18 pages, 9 figures; version accepted for publication in PR

New phase structure of the Nambu -- Jona - Lasinio model at nonzero chemical potential

It is shown that in the Nambu -- Jona - Lasinio model at nonzero chemical potential there are two different massive phases with spontaneously broken chiral symmetry. In one of them particle density is identically zero, in another phase it is not equal to zero. The transition between phases is a phase transition of the second order.Comment: 8 pages, LaTeX, no figures

Magnetic Oscillations in Dense Cold Quark Matter with Four-Fermion Interactions

The phase structures of Nambu-Jona-Lasinio models with one or two flavours have been investigated at non-zero values of $\mu$ and $H$, where $H$ is an external magnetic field and $\mu$ is the chemical potential. In the phase portraits of both models there arise infinitely many massless chirally symmetric phases, as well as massive ones with spontaneously broken chiral invariance, reflecting the existence of infinitely many Landau levels. Phase transitions of first and second orders and a lot of tricritical points have been shown to exist in phase diagrams. In the massless case, such a phase structure leads unavoidably to the standard van Alphen-de Haas magnetic oscillations of some thermodynamical quantities, including magnetization, pressure and particle density. In the massive case we have found an oscillating behaviour not only for thermodynamical quantities, but also for a dynamical quantity as the quark mass. Besides, in this case we have non-standard, i.e. non-periodic, magnetic oscillations, since the frequency of oscillations is an $H$-dependent quantity.Comment: latex, 29 pages, 8 figure

Competition of Color Ferromagnetic and Superconductive States in a Quark-Gluon System

The possibility of color ferromagnetism in an SU(2) gauge field model is investigated. The conditions allowing a stable color ferromagnetic state of the quark system in the chromomagnetic field occupying small domains are considered. A phase transition between this state and the color superconducting state is considered. The effect of finite temperature is analyzed.Comment: 21 pages, 4 Postscript figure

Quark and pion condensation in a chromomagnetic background field

The general features of quark and pion condensation in dense quark matter with flavor asymmetry have been considered at finite temperature in the presence of a chromomagnetic background field modelling the gluon condensate. In particular, pion condensation in the case of a constant abelian chromomagnetic field and zero temperature has been studied both analytically and numerically. Under the influence of the chromomagnetic background field the effective potential of the system is found to have a global minimum for a finite pion condensate even for small values of the effective quark coupling constant. In the strong field limit, an effective dimensional reduction has been found to take place.Comment: 17 pages, 6 figure

Free Energy of an SU(2) Model of (2+1)-dimensional QCD in the Constant Condensate Background

Gluon and quark contributions to the thermodynamic potential (free energy) of a (2+1)-dimensional QCD model at finite temperature in the background of a constant homogeneous chromomagnetic field H combined with A_0 condensate are calculated. The role of the tachyonic mode in the gluon energy spectrum is discussed. A possibility of the free energy global minimum generation at nonzero values of H and A_0 condensates is investigated.Comment: LaTeX 2e, 14 pages, 6 eps figures, some miscalculations were correcte