of N -particle mesonic systems, with each expectation value entering the sum weighted by the state’s Boltzmann factor. One term in this sum, of course, is the “vacuum” expectation value where the subscript represents that the trace is still taken over all of the light degrees of freedom in QCD. The right-hand side of Equation 17 represents an important step: by decomposing the mesonic operators into products of creation and annihilation operators, the vacuum expecta- tion value can be related to the overlap of two one-particle states. Also, note here that since expectation values of the higher states enter into the thermal average multiplied by factors which are roughly powers of exp( − 2 M$_{Q}$/T ), the vacuum expectation value dominates the thermal average in the limit M ≫ T . Therefore, we have identified the leading contribution to the correlator in the vector channel. The trace over the light degrees of freedom is of course the central problem of QCD, and no analytic result exists. However, in the infinite mass limit, this has been computed on the lattice as the expectation value of two Polyakov loops [24]. The dissipative effects on this propagator have been studied, as we noted previously, by gauge-gravity duality. Our ansatz here is that these results describe well the dynamics of sufficiently heavy quarks. The path integral we wish to evaluate can be written in terms of relative and absolute coordinates as where the functional integration are over all paths satisfying X (0) = 0 , X ( τ ) = x , X ( β ) = 0 , x$_{rel}$ (0) = 0 , x$_{rel}$ ( τ ) = 0 , and x$_{rel}$ ( β ) = 0 . The right-hand side of Equation 18 can now be calculated, for any potential, with a PIMC simulation. We use the Cornell potential for the interaction between the heavy quarks. To obtain G ( τ ), the first term on the right-hand side of Eq. 18 is integrated with respect to X , yielding the diagonal value for the free-particle reduced density matrix which is inde- pendent of τ . In Figure 1 we show the mesonic correlator as a function of τ at T = 1 . 2 T$_{c}$ . 9 〈 0 | J $^{µ}$( x , τ ) J$_{µ}$ ( 0 , 0) | 0 〉 = 〈 µ, x ; τ | µ, 0 ; 0 〉$_{light}$ , (17) 〈 x , x ; τ | 0 , 0 ; 0 〉 = ∫ D X exp { −$^{∫}$ β 0 dτ M ˙ X 2 + 2 η π ∫ β 0 dτ ∫ τ 0 ds ˙ X ( τ ) ˙ X ( s ) lnsin$^{(}$ π β ( τ − s )$^{)}}$ ×$^{∫}$ D x$_{rel}$ exp { −$^{∫}$ β 0 dτ $^{[}$1 4 M ˙ x 2 rel + V ( x$_{rel}$ )$^{]}$ + η 2 π ∫ β 0 dτ ∫ τ 0 ds ˙ x$_{rel}$ ( τ ) ˙ x$_{rel}$ ( s ) lnsin$^{(}$ π β ( τ − s )$^{)}}$ , (18)