First calculations which use the internal energy obtained in our calculations [@Shuryak:2004tx; @Wong:2004kn; @Brown:2004qi; @Park:2005nv] support this expectation. Most of these studies consider so far quenched QCD. Using potentials from the quenched theory, however, will describe the interaction of a heavy quark anti-quark pair in a thermal medium made up of gluons only. It is then important to understand how these results might change for the case of a thermal heat bath which also contains dynamical quarks.

On the other hand, it is the large distance property of the heavy quark interaction which is important for our understanding of the bulk properties of the QCD plasma phase, [*e.g.*]{} the screening property of the quark gluon plasma [@Kaczmarek:1999mm; @Kaczmarek:2004gv], the equation of state [@Beinlich:1997ia; @Karsch:2000ps] and the order parameter (Polyakov loop) [@Kaczmarek:2003ph; @Kaczmarek:2002mc; @Dumitru:2004gd; @Dumitru:2003hp]. In all of these studies deviations from perturbative calculations and the ideal gas behavior are expected and were indeed found at temperatures which are only moderately larger than the deconfinement temperature. This calls for quantitative non-perturbative calculations. Also in this case most of todays discussions of the bulk thermodynamic properties of the QGP and its apparent deviations from the ideal gas behavior rely on results obtained 