rather complicated expression. For the potentials which describe quarkonium spectroscopy with some precision, analytic work becomes entirely impractical. We would like to use nu- merical simulation to obtain reliable estimates of reduced density matrices and Euclidean correlators. The most natural numerical approach for the formalism we adopted is path-integral Monte Carlo (PIMC). For an excellent review of the technique, see the review of D. M. Ceperley [23]. Paths are either sampled according to a Metropolis algorithm determined by the action of interest, or sampled from some convenient distribution which samples the entire space of paths with some weight. For our work with a single degree of freedom, we found that sampling a convenient distribution (in our case, the distribution of paths determined by exp( − S$_{free}$ [ x ])) to be sufficient, which is easily sampled for any discretization of the path with a bisection method. When sampling the space of paths, the next step is to determine an estimate for the action of each path. For our case, the primitive action with the simplest integration of the new dissipative terms is sufficient. Once this is determined, any correlator can be calculated by sampling paths and making weighted averages. We should now apply this functional integral to the problem of quarkonium at tempera- tures above deconfinement. To this end, let us rework the Euclidean correlators calculated on the lattice to a form with which we can calculate. For a given channel, the two-point Euclidean correlator for a composite mesonic operator is given by where Ω = 1 , γ $^{0}$, γ $^{µ}$, γ $^{0}$γ µ determine the mesonic channel to be scalar, pseudo-scalar, vector, or pseudo-vector, respectively. For now, consider only the vector channel (the following arguments must be modified for the scalar and pseudo-vector channels). In order to switch to a first-quantization approach for the energy range where a potential model would be appropriate, think of this correlator as being the sum of the expectation values of an operator over all of the states in the Fock space 8 G ( τ, T ) = ∫ d $^{3}$x 〈 J$_{Ω}$ ( x , τ ) J$_{Ω}$ ( 0 , 0) 〉$_{β}$ , J$_{Ω}$ ( x , τ ) = ¯ ψ ( x , τ )Ω ψ ( x , τ ) , (16) III. QUARKONIUM AS AN OPEN QUANTUM SYSTEM