  We study how heavy quark dynamics is affected by the nature of the bulk
evolution of the QCD matter, the initial condition of the system, and the
treatment of elementary interactions between heavy quarks and the surrounding
medium. For the same initial condition and the same QGP expansion scenario we
discuss the consequences of the assumption of a local equilibrium by comparing
the consequences for the nuclear modification factor and the elliptic flows of
charm quarks. For this purpose we employ the parton-hadron-string dynamics
(PHSD), which is an off-shell microscopic transport approach, as well as the
linearized-Boltzmann (LB) scheme obtained by coarse graining the PHSD bulk and
assuming local equilibrium for the interactions of the charm quarks with the
bulk. The $R_{\rm AA}$ of charm quarks stemming from the later LB approach is
also compared to a genuine fluid dynamics evolution initiated by the coarse
grained PHSD, which allows to further assess the consequences of reducing the
full n-body dynamics. We then proceed to a systematic comparison of PHSD with
MC@HQ, another transport model for heavy flavors which also relies on LB
approach. In particular, we investigate the consequences for the nuclear
modification factor of charm quarks if we vary separately the initial heavy
quark distribution function in matter, the expansion dynamics of the QGP and
the elementary interactions of heavy quarks of these models. We find that the
results for both models vary significantly depending on the details of the
calculation. However, both models achieve very similar predictions for key
heavy quark observables for certain combinations of initial condition, bulk
evolution and interactions. We conclude that this ambiguity limits our ability
to determine the different properties of the system based on the current set of
observables.
