  We propose an open quantum systems approach to the physics of heavy quarkonia
in a thermal medium, based on stochastic quantum evolution. This description
emphasizes the importance of collisions with the environment and focuses on the
concept of spatial decoherence of the heavy quarkonium wave function. It is
shown how to determine the parameters of the dynamical evolution, i.e. the real
potential and the noise strength, from a comparison with quantities to be
obtained from lattice QCD. Furthermore the imaginary part of the lattice QCD
heavy quark potential is found to be naturally related to the strength of the
noise correlations. We discuss the time evolution of $Q\bar{Q}$ analytically in
a limiting scenario for the spatial decoherence and provide a qualitative
1-dimensional numerical simulation of the real-time dynamics.
