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The properties of two-flavored massless Nambu-Jona-Lasinio model in (1+1)-dimensional $R^1times S^1$ spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials $mu_I$, $mu$. The consideration is performed in the large $N_c$ limit, where $N_c$ is the number of colored quarks. It is shown that at $L=infty$ ($L$ is the length of the circumference $S^1$) the pion condensation (PC) phase with {it zero quark number density} is realized at arbitrary nonzero $mu_I$ and for rather small values of $mu$. However, at arbitrary finite values of $L$ the phase portrait of the model contains the PC phase with {it 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 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 $L$.
In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $mu$ using dimensional regularization. The ph
We study the effect of periodic boundary conditions on chiral symmetry breaking and its restoration in Quantum Chromodynamics. As an effective model of the effective potential for the quark condensate, we use the quark-meson model, while the theory i
We investigate the possibility of spatially inhomogeneous chiral and Cooper, or superconducting, pairing in the (1+1)-dimensional model by Chodos et al [ Phys. Rev. D61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is
The Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model with imaginary chemical potential is studied. The model possesses the extended ${mathbb Z}_{3}$ symmetry that QCD does. Quantities invariant under the extended ${mathbb Z}_{3}$ symmetry, suc
We present the thermodynamic properties of strongly interacting matter in finite volume in the framework of Polyakov loop enhanced Nambu$-$Jona-lasinio model within mean field approximation. We considered both the 2 flavor and 2+1 flavor matter. Our