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Dynamical Quarkonia Suppression in a QGP-Brick

I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark ($Q-\bar Q$) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schrödinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears. For those temperatures in which bound states survive in the medium, I find a non-trivial dependence of the production of excited quarkonia states on the in-medium levels, due to the mixing of vacuum and in-medium wave functions. This mixing leads, in particular, to the enhancement of the relative abundance of 2S to 1S states for those systems in which the in-medium ground state of the $Q-\bar Q$ system is dissolved or close to threshold. I also explore quarkonia production in a non-homogeneous expanding medium and find that the finite formation time effects arising from the low binding energies of in-medium states lead to the insensitivity of the heavy mesons yield to the hottest part of the system evolution.