Heavy Quark Dynamics in the QGP and Temperature Dependence of the Interaction within a Langevin and a Boltzmann Approach

One of the primary aims of the ongoing nuclear collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies is to create a Quark Gluon Plasma (QGP). The heavy quarks (HQ), charm and bottom constitutes a unique probe of the QGP properties. Both at RHIC and LHC energies a puzzling relation between the nuclear modification factor R_AA(p_T) and the elliptic flow v_2(p_T) related to heavy quark has been observed which challenged all the existing models. We discuss, within a Langevin and a Boltzamann approach, how the temperature dependence of the heavy quark drag coefficient is responsible to address for a large part of such a puzzle. We point out that for the same R_AA(p_T) one can generate 2-3 times more v_2 depending on the temperature dependence of the heavy quark drag coefficient. A drag coefficient which increases as the temperature approaches to the critical value (T_c) is a major ingredient for a simultaneous description of R_AA(p_T) and v_2(p_T). The impact of differen realization of the fluctuation-dissipation theorem on the HQ observables including the heavy-flavor pair correlations will be also addressed.