Response functions of hot and dense matter in the Nambu-Jona-Lasino model
arXiv:1809.05863 · doi:10.1088/1674-1137/43/9/094103
Abstract
We investigate the current-current correlation functions or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. We study the linear response by using the functional path integral approach and introducing the conjugated gauge fields as external sources. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for the equilibrium thermodynamics: the mean-field theory and a beyond-mean-field theory taking into account the mesonic contributions. The response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation. We show that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the Self-Energy or Density-of-State contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to treat carefully the linear terms in the external sources and the induced perturbations. These contributions from the mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover.
arXiv comment30 pages, 7 figures, submitted to Chinese Physics C!
References in corpus (78)
- Exact evolution equation for the effective potential
- Theory of ultracold Fermi gases
- QCD Phenomenology based on a Chiral Effective Lagrangian
- Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
- Color superconductivity in dense quark matter
- NJL-model analysis of dense quark matter
- The equation of state in (2+1)-flavor QCD
- The chiral and deconfinement aspects of the QCD transition
- The phase diagram of dense QCD
- The QCD equation of state with dynamical quarks
- Chiral effective model with the Polyakov loop
- Phases of QCD: lattice thermodynamics and a field theoretical model
- Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III
- BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids
- QCD at finite isospin density
- Polyakov loop, diquarks and the two-flavour phase diagram
- Superconductivity by long-range color magnetic interaction in high-density quark matter
- Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the Polyakov loop
- The Quark-Gluon Plasma in Equilibrium
- Resonantly-paired fermionic superfluids
- Thermodynamics of the BCS-BEC crossover
- Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops
- Chiral symmetry breaking in continuum QCD
- The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems
- Superconductivity from perturbative one-gluon exchange in high density quark matter
- Susceptibilities and speed of sound from PNJL model
- Lattice QCD at Finite Density -- An introductory review
- Hard-thermal-loop Resummation of the Free Energy of a Hot Gluon Plasma
- Pion Superfluidity and Meson Properties at Finite Isospin Density
- Quantum Fluctuations in the Superfluid State of the BCS-BEC Crossover
- Color superconductivity in weak coupling
- On the relation of quark confinement and chiral symmetry breaking
- BCS-BEC crossover at finite temperature for superfluid trapped Fermi atoms
- Epsilon expansion for a Fermi gas at infinite scattering length
- Two lectures on color superconductivity
- Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
- 2+1 Flavor Polyakov--Nambu--Jona-Lasinio Model at Finite Temperature and Nonzero Chemical Potential
- Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance
- Gaps and Critical Temperature for Color Superconductivity
- Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop
- On the Perturbative Nature of Color Superconductivity
- BEC-BCS Crossover in the Nambu--Jona-Lasinio Model of QCD
- Universal thermodynamics of strongly interacting Fermi gases
- BCS-BEC crossover at finite temperature in the broken-symmetry phase
- Two flavor chiral phase transition from nonperturbative flow equations
- Large-N expansion for unitary superfluid Fermi gases
- Hard-thermal-loop Resummation of the Thermodynamics of a Hot Gluon Plasma
- Pairing fluctuations and the superfluid density through the BCS-BEC crossover
- Pion condensation in electrically neutral cold matter with finite baryon density
- Color Superconductivity at Moderate Baryon Density
- Pion condensation in quark matter with finite baryon density
- Hard-thermal-loop Resummation of the Free Energy of a Hot Quark-Gluon Plasma
- NNLO hard-thermal-loop thermodynamics for QCD
- Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures
- Phase Structure of Nambu-Jona-Lasinio Model at Finite Isospin Density
- Gluon Thermodynamics at Intermediate Coupling
- The Transition Temperature to the Superconducting Phase of QCD at High Baryon Density
- Three-flavor Nambu--Jona-Lasinio model at finite isospin chemical potential
- How the quark self-energy affects the color-superconducting gap
- Pion Condensation in Baryonic Matter: from Sarma Phase to Larkin-Ovchinnikov-Fudde-Ferrell Phase
- Precursor of Color Superconductivity in Hot Quark Matter
- Three-loop HTL gluon thermodynamics at intermediate coupling
- Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model
- Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories
- Gauge Field Fluctuations and First-Order Phase Transition in Color Superconductivity
- Quark Spectrum above but near Critical Temperature of Chiral Transition
- Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids
- Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state and Leggett mode
- Reduced quantum anomaly in a quasi-2D Fermi superfluid: The significance of the confinement-induced effective range of interactions
- Pion dissociation and Levinson's theorem in hot PNJL quark matter
- Electrical Conductivity of Dense Quark Matter with Fluctuations and Magnetic Field Included
- Dynamic density and spin responses of a superfluid Fermi gas in the BCS-BEC crossover: Path integral formulation and pair fluctuation theory
- Mott dissociation of pions and kaons in hot, dense quark matter
- Fluctuation and Dissipation of Axial Charge from Massive Quarks
- Correcting inconsistencies in the conventional superfluid path integral scheme
- The Compressibility in Strongly Correlated Superconductors and Superfluids: From BCS to BEC
- Gauge invariant theories of linear response for strongly correlated superconductors
- Fluctuation sound absorption in quark matter