  Decoherence dynamics of quarkonia is studied in the high-temperature
deconfined phase of SU($N_c$) gauge theories. In particular, we analyze the
symmetry properties of SU($N_c$) stochastic potential model and find a novel
"event-by-event" symmetry for $N_c=2$ case, similar to the $G$-parity of
hadronic systems. This novel symmetry constrains the relation between diagonal
and off-diagonal components of quarkonium density matrix, leaving the latter to
be finite at late times. We also present one-dimensional numerical simulation
of the model, which indicates the usefulness of the complex potential
simulations for the quarkonium survival probabilities in relativistic heavy-ion
collisions, provided that the effect of dissipation can be neglected.
