  In the quark-gluon plasma (QGP), it is well known that the evolution of
quarkonia is affected by the screening of the interaction between the quark and
the anti-quark. In addition, exchange of energy and color with the surrounding
medium can be included via the incorporation of noise terms in the evolution
Hamiltonian. For noise correlated locally in time, these dynamics have been
studied in a simple setting by Kajimoto et al.[PHYS. REV. D 97, 014003(2018)].
We extend this calculation by considering non-Abelian dynamics for a
three-dimensional wavefunction. We also propose a modification of the noise
correlation, allowing it to have a finite correlation in time with the
motivation to include long-lived gluonic correlations. We find that in both
cases the results differ significantly from solutions of rate equations.
