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Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma

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.