  By coupling the Boltzmann transport equations of both quarkonium and open
heavy quarks, we investigate their dynamical evolution inside the quark-gluon
plasma and study quarkonium production in heavy ion collisions. The Boltzmann
transport equation of quarkonium is derived from the open quantum system
formalism and effective field theory of QCD by assuming quarkonium interacts
weakly with the plasma. The dissociation and recombination terms in the
Boltzmann equation are calculated in potential nonrelativistic QCD. It is shown
that the combination of quarkonium dissociation, recombination, open heavy
quark diffusion and energy loss can drive the system of quarkonium and open
heavy quarks to detailed balance and kinetic thermalization. By solving the
transport equations with initial momenta of quarkonia and heavy quarks sampled
from PYTHIA and a hydrodynamic medium, we can calculate the nuclear
modification factors of bottomonium and describe the data at both RHIC and LHC
energies. The azimuthal angular anisotropy coefficient $v_2$ of $\Upsilon$(1S)
in 5.02 TeV peripheral Pb-Pb collisions is also predicted.
