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Register a new userFinite-size effects in pion condensation phenomena of dense baryonic matter in the NJL$_2$ model
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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 $L$.
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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 phase diagram in the $mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $mu>mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $mu_I$. The phase diagram in the $mu_I$--$mu$ plane is mapped out and shows a rich phase structure.
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 is quantized in a cubic box of size $L$. After specifying a renormalization prescription for the vacuum quark loop, we study the condensate at finite temperature, $T$, and quark chemical potential, $mu$. We find that lowering $L$ leads to a catalysis of chiral symmetry breaking. The excitation of the zero mode leads to a jump in the condensate at low temperature and high density, that we suggest to interpret as a gas-liquid phase transition that takes place between the chiral symmetry broken phase (hadron gas) and chiral symmetry restored phase (quark matter). We characterize this intermediate phase in terms of the increase of the baryon density, and of the correlation length of the fluctuations of the order parameter: for small enough $L$ the correlation domains occupy a substantial portion of the volume of the system, and the fluctuations are comparable to those in the critical region. For these reasons, we dub this phase as the {it subcritical liquid}. The qualitative picture that we draw is in agreement with previous studies based on similar effective models. We also clarify the discrepancy on the behavior of the critical temperature versus $L$ found in different models.
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 performed at nonzero temperature $T$ and quark number chemical potential $mu$. It is shown in the framework of the Fulde--Ferrel inhomogeneity ansatz for chiral and Cooper condensates that if $G_1>G_2$, where $G_1$ and $G_2$ are the coupling constants in the quark-antiquark and diquark channels, then in the $(mu,T)$-phase diagram the superconducting phase is suppressed by spatially inhomogeneous chiral spiral phase with broken chiral symmetry. In contrast, in the above mentioned original Chodos et al model, where only the opportunity for homogeneous condensates were taken into account, the superconducting phase is realized at sufficiently high values of $mu$ at arbitrary values of $G_2>0$, including the interval $0<G_2<G_1$.
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, such as the partition function, the chiral condensate and the modified Polyakov loop, have the Roberge-Weiss (RW) periodicity. The phase diagram of confinement/deconfinement transition derived with the PNJL model is consistent with the RW prediction on it and the results of lattice QCD. The phase diagram of chiral transition is also presented by the PNJL model.
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 primary observation was a qualitative change in the phase transition properties that resulted in the lowering of the temperature corresponding to the critical end point. This would make it favorable for detection in heavy-ion experiments that intend to create high density matter with considerably small temperatures. We further demonstrate the possibility of obtaining chiral symmetry restoration even within the confined phase in finite volumes.
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