  The production and space-time evolution of charm and bottom quarks in
nucleus-nucleus collisions at RHIC and LHC are investigated with the partonic
transport model BAMPS (Boltzmann Approach of MultiParton Scatterings). Heavy
quarks, produced in primary hard parton scatterings during nucleon-nucleon
collisions, are sampled using the Monte Carlo event generator PYTHIA or the
leading order mini-jet model in conjunction with the Glauber model, revealing a
strong sensitivity on the parton distribution functions, scales, and heavy
quark mass. In a comprehensive study exploring different charm masses, K
factors, and possible initial gluon conditions, secondary production and the
evolution of heavy quarks are examined within a fully dynamic BAMPS simulation
for central heavy ion collisions at RHIC and LHC. Although charm production in
the quark-gluon plasma can be neglected at RHIC, it is significant at LHC but
very sensitive to the initial conditions and the charm mass. Bottom production
in the quark-gluon plasma, however, is negligible both at RHIC and LHC.
