  We investigate the thermalization of charm quarks in high energy heavy ion
collisions. To this end, we calculate the diffusion coefficient in the
perturbative Quark Gluon Plasma and relate it to collisional energy loss and
momentum broadening. We then use these transport properties to formulate a
Langevin model for the evolution of the heavy quark spectrum in the hot medium.
The model is strictly valid in the non-relativistic limit and for all
velocities $\gamma v < \alphas^{-1/2}$ to leading logarithm in $T/m_D$. The
corresponding Fokker-Planck equation can be solved analytically for a Bjorken
expansion and the solution gives a simple estimate for the medium modifications
of the heavy quark spectrum as a function of the diffusion coefficient. Finally
we solve the Langevin equations numerically in a hydrodynamic simulation of the
heavy ion reaction. The results of this simulation are the medium modifications
of the charm spectrum $R_{AA}$ and the expected elliptic flow $v_2(p_T)$ as a
function of the diffusion coefficient.
