I. INTRODUCTION Because of the masses of heavy quarks relative to the QCD energy scale Λ$_{QCD}$, heavy- heavy bound states are systems which can be described to some accuracy with first quanti- zation techniques [1–3]. At zero temperature, lattice calculations of a heavy-heavy system give a potential term which can describe quarkonium spectroscopy. The potential has a non- trivial temperature dependence. For this reason, it has been the hope of both theorists and experimentalists for over twenty years that changes in the yields of quarkonium in heavy-ion collisions would be a signal for changes in the temperature and phase of the medium [4]. Since then, analysis of heavy-ion experiments have shown that some suppression of J/ψ yields at the RHIC is anomalous [5]. However, there is little agreement among theorists over the cause of this suppression. It is clear that the dynamics of quarkonium above the deconfinement phase transition should be considered carefully. One step in this direction was made by Shuryak and one of us, who modeled charmo- nium in heavy-ion collisions as undergoing Brownian motion, with the heavy quark diffusion coefficient D$_{H}$ taken to be quite small, as expected from phenomenology of single heavy quarks [8, 9] and by gauge-gravity duality [10–12]. This work [7] demonstrated that the survival of J/ψ states in plasma cannot be determined just by examining whether or not the temperature-dependent potentials allow bound states; instead, the dynamics of charm and charmonium are determined by multiple interactions with the medium, and the time scales of the collision are very important. Another important step in understanding the dynamics of charmonium is provided by newer lattice calculations [6]. In these calculations, the Euclidean correlators for local operators related to quarkonium spectroscopy are calculated, namely, G ( τ, T ) = ∫ d $^{3}$x 〈 J$_{H}$ ( x , τ ) J$_{H}$ ( 0 , 0) 〉 , where J$_{H}$ ( x , τ ) = ¯ ψ ( x , τ )Γ ψ ( x , τ ) is a local composite operator related to a given mesonic channel. Taking the results of these lattice simulations, Mocsy and Petreczky compared these correlators, at various temperatures and in different channels, with the results of two different potential models [13]. In this work, there is a low-frequency contribution to the spectral densities used to determine the Euclidean correlator, which is due to the diffusion of heavy quarks [14], however, for ω ≫ T $^{2}$/M , the diffusion of heavy quarks is assumed not to have any effect on the dynamics of quarkonium. In this paper, we will outline how the imaginary-time propagator with periodicity β = 1 /T 2