scholarly journals Confining density functional approach for color superconducting quark matter and mesonic correlations

2022 ◽  
Vol 258 ◽  
pp. 07008
Author(s):  
Oleksii Ivanytskyi ◽  
David Blaschke ◽  
Konstantin Maslov
Keyword(s):  
Quark Matter ◽  
Density Functional ◽  
Gaussian Approximation ◽  
Compact Star ◽  
Mean Field ◽  
Functional Approach ◽  
Meson Mass ◽  
Observational Constraints ◽  
The Mean ◽  
Meson Mass Spectrum

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Beyond the mean field, quark correlations in the pseudoscalar channel are described within the Gaussian approximation. This explicitly introduces pionic states into the model. Their contribution to the thermodynamic potential is analyzed within the Beth–Uhlenbeck framework. The modification of the meson mass spectrum in the vicinity of thee (de)confinement transition is interpreted as the Mott transition. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

THE MOTT TRANSITION AND F ELECTRON PHYSICS

2003 ◽  
Vol 17 (28) ◽  
pp. 5101-5109 ◽  
Author(s):  
GABRIEL KOTLIAR ◽  
SERGEJ Y. SAVRASOV
Keyword(s):  
Field Theory ◽  
Spectral Density ◽  
Density Functional ◽  
Mean Field Theory ◽  
Mean Field ◽  
Mott Transition ◽  
Functional Approach ◽  
Dynamical Mean Field Theory ◽  
Quantitative Results ◽  
Actinide Series

We revisit the issue of the Mott transition across the actinide series from the perspective of the spectral density functional approach to realistic dynamical mean-field theory. We stress both qualitative insights from the connection with models and quantitative results.

scholarly journals PAIRING CORRELATIONS BEYOND THE MEAN FIELD

2007 ◽  
Vol 16 (02) ◽  
pp. 222-236 ◽  
Author(s):  
M. BENDER ◽  
T. DUGUET
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Mean Field ◽  
Energy Functional ◽  
Functional Theory ◽  
Self Consistent ◽  
Configuration Mixing ◽  
Pairing Correlations ◽  
The Mean

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.

σ AND ω, WITH ∆-BARYON, AT HIGH TEMPERATURE

1996 ◽  
Vol 05 (03) ◽  
pp. 511-520
Author(s):  
ABHIJIT BHATTACHARYYA
Keyword(s):  
High Temperature ◽  
Temperature Dependence ◽  
Random Phase Approximation ◽  
Random Phase ◽  
Mean Field ◽  
Meson Mass ◽  
Phase Approximation ◽  
Effective Masses ◽  
The Mean ◽  
Walecka Model

The temperature dependence of σ and ω meson effective masses due to the presence of Δ-baryon has been studied. Starting from the Walecka model, containing both nucleon and Δ, the temperature dependence of effective masses of nucleon and Δ have been calculated at the Mean Field (MF) level. These results have been used to calculate the contribution to the effective masses of σ and ω from both [Formula: see text]- and [Formula: see text]-loops in Random Phase Approximation (RPA). The results are quite interesting. The σ-meson mass increases due to the [Formula: see text] loop whereas it decreases due to [Formula: see text]-loop with temperature. Further, the change in σ-meson mass due to [Formula: see text]-loop is much more compared to that due to [Formula: see text]-loop. For the ω-meson, both the loops are responsible for the increase in mass with temperature.

MEAN FIELD APPROACH TO THE GAP OF A MODEL INTERACTING SYSTEM

1988 ◽  
Vol 02 (01) ◽  
pp. 87-101
Author(s):  
KAJOLI BANERJEE ◽  
VIJAY A. SINGH ◽  
G. R. BHAT
Keyword(s):  
Density Functional ◽  
Local Density ◽  
Mean Field ◽  
Functional Theory ◽  
One Dimensional ◽  
Coulomb Term ◽  
The Density Functional Theory ◽  
The Mean ◽  
Transfer Term ◽  
Mean Field Approximations

The well-known local density approximation severely underestimates the gap of insulating materials. We undertake a study of an infinite one-dimensional model interacting system where the gap is known exactly. We use variational procedures, similar in spirit to Hohenberg and Kohn's derivation of the density functional theory. The mean field approximations so obtained are used to calculate the gap in the eigenspectrum. The gap is found to be systematically underestimated for realistic values of the parameters (u/t ≤ 4 where u is the Coulomb term and t, the transfer term). For u/t > 4, the approximate gap is in close agreement with the exact gap. The underestimation of the gap is investigated with respect to the discontinuity in the effective potential.

The renormalization group (RG) approach: The critical theory near four dimensions

2021 ◽  
pp. 357-390
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Gaussian Approximation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Flow Equations ◽  
Four Dimensions ◽  
The Mean

In Chapter 14, the singular behavior of ferromagnetic systems with O(N) symmetry and short-range interactions, near a second order phase transition has been determined in the mean-field approximation, which is also a quasi-Gaussian approximation. The mean-field approximation predicts a set of universal properties, properties independent of the detailed structure of the microscopic Hamiltonian, the dimension of space, and, to a large extent, of the symmetry of systems. However, the leading corrections to the mean-field approximation, in dimensions smaller than or equal to four, diverge at the critical temperature, and the universal predictions of the mean-field approximation cannot be correct. Such a problem originates from the non-decoupling of scales and leads to the question of possible universality. In Chapter 9, the question has been answered in four dimensions using renormalization theory, and related renormalization group (RG) equations. Moreover, below four dimensions, in an expansion around the mean-field, the most singular terms near criticality can be also formally recovered from a continuum, low-mass φ4 field theory. More generally, following Wilson, to understand universality beyond the mean-field approximation, it is necessary to build a general renormalization group in the form of flow equations for effective Hamiltonians and to find fixed points of the flow equations. Near four dimensions, the flow equations can be approximated by the renormalization group of quantum field theory (QFT), and the fixed points and critical behaviours derived within the framework of the Wilson-Fisher ϵ expansion.

scholarly journals PHASE DIAGRAM OF TWO-FLAVOR QUARK MATTER: GLUONIC PHASE AT NONZERO TEMPERATURE

2009 ◽  
Vol 24 (09) ◽  
pp. 647-658
Author(s):  
O. KIRIYAMA
Keyword(s):  
Phase Diagram ◽  
Quark Matter ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Nonzero Temperature ◽  
Self Consistent ◽  
Consistent Manner ◽  
Cylindrical Phase ◽  
The Mean

The phase structure of neutral two-flavor quark matter at nonzero temperature is studied. Our analysis is performed within the framework of a gauged Nambu–Jona-Lasinio model and the mean-field approximation. We compute the free energy of the gluonic phase (gluonic cylindrical phase II) in a self-consistent manner and investigate the phase transition from the gluonic phase to the 2SC/g2SC/NQ phases. We briefly consider the phase diagram in the plane of coupling strength versus temperature and discuss the mixed phase consisting of the normal quark and 2SC phases.

INTERACTION EFFECTS IN THE EQUATION OF STATE OF BARYONIC AND QUARK MATTER FOR DENSE STARS

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1505-1510
Author(s):  
F. L. BRAGHIN
Keyword(s):  
Equation Of State ◽  
Quark Matter ◽  
Mean Field ◽  
Dynamic Equations ◽  
Field Equations ◽  
Analytical Treatment ◽  
Mean Field Equations ◽  
The Mean ◽  
Dense Stars ◽  
Self Consistency

Some specific aspects of the equation of state of strongly interacting baryonic and quark matter are addressed by substituting (at least in part) the usual numerical self-consistency of the mean field equations, eventually with corrections, by an analytical treatment of the dynamic equations of the components of such system. Several solutions can be found yielding different behaviors. The mean field solutions are partially extended.

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