  Quark Gluon Plasma transport coefficients for heavy quarks and
quark-antiquark pairs are computed through an extension of the results obtained
for a hot QED plasma by describing the heavy-quark propagation in the eikonal
approximation and by weighting the gauge field configurations with the Hard
Thermal Loop effective action. It is shown that such a model allows to
correctly reproduce, at leading logarithmic accuracy, the results obtained by
other independent approaches. The results are then inserted into a relativistic
Langevin equation allowing to follow the evolution of the heavy-quark momentum
spectra. Our numerical findings are also compared with the ones obtained in a
strongly-coupled scenario, namely with the transport coefficients predicted
(though with some limitations and ambiguities) by the AdS/CFT correspondence.
