  We study the properties of the Lindbladian quantum mechanical evolution of
quarkonia with non-Abelian charges (color-singlet and octet) in the quark-gluon
plasma. We confirm that heavy quark recoils in the Lindblad equation correctly
thermalize quarkonium colorful states within statistical errors from the
simulation method. We also demonstrate that the Lindblad equation in the dipole
limit can provide an efficient alternative method, which is applicable to a
finite time evolution before thermalization and dramatically reduces the
numerical cost. Our findings will serve as a foundation for large-scale
simulation of quarkonium dynamics in the relativistic heavy-ion collisions.
