Pion condensation at finite temperature

Kolehmainen, Karen; Baym, Gordon

doi:10.1016/0375-9474(82)90359-1

Cited by 27 publications

(11 citation statements)

References 15 publications

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“…At very high temperatures (T > ∼ 50 MeV for symmetric nuclear matter) thermal excitations of the pionic degrees of freedom, the 'thermal pions' [80] become important and should be explicitly included in the equation of state [81]. Our present calculations do not have any explicit non-nucleonic degrees of freedom, thus they cannot be extended to very high temperatures without the explicit inclusion of the thermal pions.…”

Section: Discussionmentioning

confidence: 98%

Variational theory of hot nucleon matter. II. Spin-isospin correlations and equation of state of nuclear and neutron matter

Mukherjee

2009

Phys. Rev. C

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We apply the variational theory for fermions at finite temperature and high density, developed in an earlier paper, to symmetric nuclear matter and pure neutron matter. This extension generalizes to finite temperatures, the many body technique used in the construction of the zero temperature Akmal-Pandharipande-Ravenhall equation of state. We discuss how the formalism can be used for practical calculations of hot dense matter. Neutral pion condensation along with the associated isovector spin longitudinal sum rule is analyzed. The equation of state is calculated for temperatures less than 30 MeV and densities less than three times the saturation density of nuclear matter. The behavior of the nucleon effective mass in medium is also discussed.

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Section: Discussionmentioning

confidence: 98%

Variational theory of hot nucleon matter. II. Spin-isospin correlations and equation of state of nuclear and neutron matter

Mukherjee

2009

Phys. Rev. C

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“…(24). One has to represent Q †Q as a matrix, where the rows and columns correspond to the plane-wave basis functions of the fermionic fields e ∓ı(k0x0+k1x1) / L 0L1 [cf.…”

Section: Discussionmentioning

confidence: 99%

“…One of the simplest non-constant field configurations is the so-called chiral density wave (CDW) which, in chiral hadronic models, corresponds to a one-dimensional condensate of the form σ(x 3 ) = φ cos(px 3 ) together with pion condensation, π 0 (x 3 ) = φ sin(px 3 ). Various studies have found that the CDW is favorable compared to a constant condensate at sufficiently high densities [15][16][17][18][19][20][21][22][23][24][25][26]. Interestingly, a CDW has recently also been obtained within the extended Linear Sigma Model [27], which is a general chiral hadronic model with (axial-)vector degrees of freedom [4,5].…”

Section: Introductionmentioning

confidence: 99%

Inhomogeneous condensation in effective models for QCD using the finite-mode approach

et al. 2016

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We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for 1 + 1 dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in 3 + 1 dimensions is investigated and its phase diagram is determined with particular focus on the inhomogeneous phase at high density.

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“…In hadronic nuclear matter the existence of spatially inhomogenous phases is familiar, as pionic [26][27][28][29][30][31][32][33][34][35][36][37][38][39] and kaonic [40][41][42][43] condensates. They are ubiquitous in Gross-Neveu models in 1 + 1 dimensions, which are soluble either for a large number of flavors [44][45][46][47][48][49] or by using advanced nonperturbative techniques [50].…”

Section: Introductionmentioning

confidence: 99%

Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics

2019

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We consider the phase diagram of hadronic matter as a function of temperature, T , and baryon chemical potential, µ. Currently the dominant paradigm is a line of first order transitions which ends at a critical endpoint.In this work we suggest that spatially inhomogenous phases are a generic feature of the hadronic phase diagram at nonzero µ and low T . Familiar examples are pion and kaon condensates. At higher densities, we argue that these condensates connect onto chiral spirals in a quarkyonic regime.Both of these phases exhibit the spontaneous breaking of a global U (1) symmetry and quasi-long range order, analogous to smectic liquid crystals. We argue that there is a continuous line of first order transitions which separate spatially inhomogenous from homogenous phases, where the latter can be either a hadronic phase or a quark-gluon plasma.While mean field theory predicts that there is a Lifshitz point along this line of first order transitions, in three spatial dimensions strong infrared fluctuations wash out any Lifshitz point.Using known results from inhomogenous polymers, we suggest that instead there is a Lifshitz regime. Non-perturbative effects are large in this regime, where the momentum dependent terms for the propagators of pions and associated modes are dominated not by terms quadratic in momenta, but quartic. Fluctuations in a Lifshitz regime may be directly relevant to the collisions of heavy ions at (relatively) low energies, √ s/A : 1 → 20 GeV. A quarkyonic phase only exists when quark excitations near the Fermi surface are (effectively) confined. While for three colors numerical simulations of lattice gauge theories at nonzero quark density are afflicted by the sign problem for three colors, they are possible for two colors [118-123]. Although the original argument for a quarkyonic phase was based upon the limit of a large number of colors [102], these simulations show that even for two colors, the expectation value of the Polyakov loop is small, indicating confinment, up to large values of the quark chemical potential [118-123]. Directly relevant to our analysis are the results of Bornyakov et al., who find that the string tension decreases gradually from its value in vacuum, to essentially zero at µ q ∼ 750 MeV: see Fig. 3 of Ref. [123]. This suggests

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Pion condensation at finite temperature

Cited by 27 publications

References 15 publications

Variational theory of hot nucleon matter. II. Spin-isospin correlations and equation of state of nuclear and neutron matter

Variational theory of hot nucleon matter. II. Spin-isospin correlations and equation of state of nuclear and neutron matter

Inhomogeneous condensation in effective models for QCD using the finite-mode approach

Fluctuations in cool quark matter and the phase diagram of quantum chromodynamics

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