  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.
