Abstract
In this manuscript we review the basic concepts related to the study of the dynamics of the heavy quarks in quark-gluon plasma created in ultra-relativistic heavy-ion collisions. We discuss the relevant physical scale as well as the difficulties of the present theoretical approach with an aim to have a self-consistent description of the experimental data at both RHIC and LHC. In the second part we challenge the assumption of brownian motion for charm quarks and compare the dynamical evolution of charm and bottom quarks in the Fokker-Planck approach with the Boltzmann Transport calculationone. We show that while for bottom the motion appears quite close to a Brownian one, this does note seems to be the case for charms quarks. In particular the solution of the full two-body collision integral shows that the anisotropic flows are large with respect to those predicted by a Langevin dynamics. We show that using isotropic cross section one may describe the suppression RAA and elliptic flow v2 simultaneously.
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