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We investigate the current-current correlation functions or the so-calledresponse functions of a two-flavor Nambu-Jona-Lasino model at finitetemperature and density. We study the linear response by using the functionalpath integral approach and introducing the conjugated gauge fields as externalsources. The response functions can be obtained by expanding the generationalfunctional in powers of the external sources. We derive the response functionsparallel to two well-established approximations for the equilibriumthermodynamics: the mean-field theory and a beyond-mean-field theory takinginto account the mesonic contributions. The response functions based on themean-field theory recover the so-called quasiparticle random phaseapproximation. We calculate the dynamical structure factors for the densityresponses in various channels within the random phase approximation. We showthat the dynamical structure factors in the baryon axial vector and isospinaxial vector channels can be used reveal the quark mass gap and the Mottdissociation of mesons, respectively. Noting that the mesonic contributions arenot taken into account in the random phase approximation, we also derive theresponse functions parallel to the beyond-mean-field theory. We show that themesonic fluctuations naturally give rise to three kinds of famous diagrammaticcontributions: the Aslamazov-Lakin contribution, the Self-Energy orDensity-of-State contribution, and the Maki-Thompson contribution. Unlike theequilibrium case, in evaluating the fluctuation contributions, we need to treatcarefully the linear terms in the external sources and the inducedperturbations. These contributions from the mesonic fluctuations are expectedto have significant effects on the transport properties of hot and dense matteraround the chiral phase transition or crossover.

Response functions of hot and dense matter in the Nambu-Jona-Lasino model