Study of hot and dense nuclear matter in effective QCD model

In this thesis we use various effective QCD models to investigate hot and dense nuclear matter created in heavy ion collisions. To characterize such matter, we mainly exploit correlation functions and some of the associated spectral properties. We explore the vector meson current-current correlation function with and without the influence of vector interaction in Nambu\textendash Jona-Lasinio (NJL) model and also in its Polyakov loop extended version (PNJL). As a spectral property we have computed the dilepton rate which is found to be enhanced in strongly interacting QGP (sQGP) as compared to the Born rate in a weakly coupled QGP. We further consider the idea of entanglement between the chiral and confinement dynamics through the entangled PNJL (EPNJL) model and re-explore the vector spectral function and the spectral property such as the dilepton production rate studied in our earlier effort. Because of the strong entanglement, the coupling strengths run with the temperature and chemical potential. The implications of such running on the dilepton rate have been discussed in details. The Euclidean vector correlator and the response of the conserved density fluctuations related with the temporal vector correlator have also been investigated. We have considered both the scenarios, i.e. presence and absence of the vector interaction. The inclusion of the vector interaction also brings forth some intriguing issues in the fluctuation of conserved density, namely the QNS. It has been discussed in details and we try to address it using EPNJL model. We also assume the QGP to be made of a non-interacting quarks, antiquarks and gluons and construct a partition function which is restricted by the assumption of a color singlet projection to conform with the $SU(3)_c$ symmetry. This type of simple quantum statistical description exhibits very interesting features, which we have discussed in details.