Phase diagram and bulk thermodynamical quantities in the Nambu–Jona-Lasinio model at finite temperature and density

Schwarz, Thomas Michael; Klevansky, S. P.; Papp, Gábor

doi:10.1103/physrevc.60.055205

Cited by 153 publications

(184 citation statements)

References 17 publications

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“…On the other hand it is known that at very high densities the ground state of QCD is a color superconductor, whereas particle-hole pairing is suppressed in this regime [38]. Moreover, NJL-model calculations for homogeneous matter typically find that the chiral phase transition at low temperature goes directly from the chirally broken phase into a color superconducting phase, at least for isospin symmetric matter [172,89,68]. It is therefore natural to ask how the chiral phase transition looks like if both possibilities, particle-hole and particle-particle pairing, are taken into account.…”

Section: Competition With Color Superconductivitymentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

241

258

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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Section: Competition With Color Superconductivitymentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

241

258

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“…If the system was in an equilibrium state at t = −∞, then the equilibrium condition dV eff (σ 0 )/dσ 0 = 0 ensures that for t < 0 there is a solution of the equations of motion (4.8) of the form 10) where…”

Section: A Linear Relaxation Of Fluctuationsmentioning

confidence: 99%

“…The finite-temperature effective potential is given by 9) and its derivative with respect to σ 0 reads 10) where n(ω k ) = 1/(e βω k + 1). The equilibrium state of the system is determined by the condition dV eff (σ 0 )/dσ 0 = 0, which leads to the gap equation…”

Section: Static Ginzburg-landau Effective Theorymentioning

confidence: 99%

“…Some popular models of chiral dynamics are the linear sigma model [5], the Gross-Neveu model [6], and the Nambu-Jona-Lasinio model [7]. The thermodynamic equilibrium aspects of these models at finite temperature and/or quark chemical potential have been studied extensively in the literature [8,9,10,11], in particular lattice gauge theory has provided an impressive body of results on the phase diagram for temperature and chemical potential (see for example [12,13,14,15]. Nevertheless, a microscopic understanding of their dynamical nonequilibrium aspects has just begun to emerge.…”

Section: Introductionmentioning

confidence: 99%

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Nonequilibrium pion dynamics near the critical point in a constituent quark model

Boyanovsky¹,

Vega²,

Wang³

2004

Nuclear Physics A

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We study static and dynamical critical phenomena of chiral symmetry breaking in a two-flavor Nambu-Jona-Lasinio constituent quark model. We obtain the low-energy effective action for scalar and pseudoscalar degrees of freedom to lowest order in quark loops and to quadratic order in the meson fluctuations around the mean field. The static limit of critical phenomena is shown to be described by a Ginzburg-Landau effective action including spatial gradients. Hence static critical phenomena is described by the universality class of the O(4) Heisenberg ferromagnet. Dynamical critical phenomena is studied by obtaining the equations of motion for pion fluctuations. We find that for T < Tc the are stable long-wavelength pion excitations with dispersion relation ωπ(k) = k described by isolated pion poles. The residue of the pion pole vanishes near Tc as Z ∝ 1/| ln(1 − T /Tc)| and long-wavelength fluctuations are damped out by Landau damping on a time scale t rel (k) ∝ 1/k, reflecting critical slowing down of pion fluctuations near the critical point. At the critical point, the pion propagator features mass shell logarithmic divergences which we conjecture to be the harbinger of a (large) dynamical anomalous dimension. We find that while the classical spinodal line coincides with that of the Ginzburg-Landau theory, the growth rate of long-wavelength spinodal fluctuations has a richer wavelength dependence as a consequence of Landau damping. We argue that Landau damping prevents a local low energy effective action in terms of a derivative expansion in real time at least at the order studied.

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“…The phenomenological value of the coupling constant G 1 in the qq Cooper channel is related to the coupling constant in the qq di-quark channel by the relation G 1 = N c /(2N c − 2)G; the latter coupling constant and the cut-off are fixed by adjusting the model to the vacuum properties of the system [26,27]. Figure 9 summarizes the main features of the color superconducting DFS phase [25].…”

Section: Flavor Asymmetric Quark Condensatesmentioning

confidence: 99%

Superconductivity With Deformed Fermi Surfaces and Compact Stars

Sedrakian¹

2006

NATO Science Series II: Mathematics, Physics and Chemistry

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I discuss the deformed Fermi surface superconductivity (DFS) and some of its alternatives in the context of nucleonic superfluids and two flavor color superconductors that may exist in the densest regions of compact stellar objects. IntroductionThe astrophysical motivation to study the superconducting phases of dense matter arises from the importance of pair correlations in the observational manifestations of dense matter in compact stars. If the densest regions of compact stars contain deconfined quark matter it must be charge neutral and in β equilibrium with respect to the Urca processes d → u + e +ν and u + e → d + ν, where e, ν, andν refer to electron, electron neutrino, and antineutrino. The u and d quarks in deconfined matter fill two different Fermi spheres which are separated by a gap of the order of electron chemical potential. At high enough densities (where the typical chemical potentials become of the order of the rest mass of a s quark), strangeness nucleation changes the equilibrium composition of the matter via the reactions s → u + e +ν and u + e → s + ν. Although the strangeness content of matter affects its u-d flavor asymmetry, the separation of the Fermi energies remains a generic feature. The dense quark matter is expected to be a color superconductor (the early work is in Refs. [1]; recent developments are summarized in the reviews [2]).Accurate description of the matter in this regime requires, first, tools to treat the Lagrangian of QCD in the nonperturbative regime and, second, an understanding of the superconductivity under asymmetry in the population of fermions that pair. The first principle lattice QCD calculations are currently not feasible for the purpose of understanding the physics of compact stars; the effective models that are used rarely incorporate all aspects of the known phenomenology like de-confinement and chiral restoration. Despite of the limitations of current models, a lot can be learned about generic features of possible

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Phase diagram and bulk thermodynamical quantities in the Nambu–Jona-Lasinio model at finite temperature and density

Cited by 153 publications

References 17 publications

Inhomogeneous chiral condensates

Inhomogeneous chiral condensates

Nonequilibrium pion dynamics near the critical point in a constituent quark model

Superconductivity With Deformed Fermi Surfaces and Compact Stars

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