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The in-medium physics of heavy quarkonium is an ideal proving ground for ourability to connect knowledge about the fundamental laws of physics tophenomenological predictions. One possible route to take is to attempt adescription of heavy quark bound states at finite temperature through aSchroedinger equation with an instantaneous potential. Here we review recentprogress in devising a comprehensive approach to define such a potential fromfirst principles QCD and extract its, in general complex, values fromnon-perturbative lattice QCD simulations. Based on the theory of open quantumsystems we will show how to interpret the role of the imaginary part in termsof spatial decoherence by introducing the concept of a stochastic potential.Shortcomings as well as possible paths for improvement are discussed.

From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma