  In this work, we investigate the melting of charmonium states within a
holographic QCD model in the context of Einstein-Maxwell-Dilaton (EMD) theory.
In the dual field theory, the model describes the heavy mesons inside a finite
temperature and density medium. First, we calculate the spectrum at zero
temperature. Then, at finite temperature, we obtain the spectral functions,
where the heavy vector meson are represented by peaks. We show that the
charmonium melts down at temperatures above the confinement/deconfinement
temperature of the quark-gluon plasma. We also observe that the chemical
potential speeds up the melting process. This finding is in agreement with
results previously reported in the literature. In the gravitational side of the
theory, we solve the perturbation equations in the hydrodynamics limit. From
this result, we read off the diffusion coefficient by comparing the dispersion
relation against the corresponding result obtained in the dual field theory. We
also investigate the behavior of the diffusion coefficient as a function of the
temperature. The perturbation equations are solved numerically, in order to get
the quasinormal frequencies. We report the emergence of a new mode whose real
part increases rapidly at a certain value of the chemical potential while its
imaginary part decreases with the increasing of the chemical potential.
Finally, by comparing against results obtained in the conformal plasma, we
observe that the real part of the frequency increases, while the imaginary part
decreases when we consider the non-conformal plasma.
