In this study, we investigate the real-time evolution of quarkonium bound states
in a quark-gluon plasma in an improved QCD based stochastic potential model. This
model describes the quarkonium dynamics in terms of a Schrödinger equation with
an in-medium potential and two noise terms encoding the residual interaction
between the heavy quarks and the medium. The time evolution described by this
equation is unitary, since the effective potential term is real-valued. At a glance this is at odds with lattice results, but we explain why this it is
actually not the case.
We discuss the the time evolution of the existence probabilities of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualitatively consistent with the experimental data in relativistic heavy-ion collisions. The other is that the noise plays an important role in order to describe quarkonium dynamics in medium, in particular it causes decoherence of the quarkonium wave function. The effectiveness of decoherence is controlled by a new length scale, correlation length of the noise. Its effect has not been included in existing phenomenological studies, and we discuss its importance in detail.
Furthermore, if time allows, we also discuss strategies to take account of dissipation effects in addition to diffusion effects caused by the residual interactions between the heavy quarks and the medium.
 S. Kajimoto, Y. Akamatsu, M. Asakawa, and A. Rothkopf, arXiv:1705.03365, Phys. Rev. D in press.
 S. Kajimoto, Y. Akamatsu, M. Asakawa, and A. Rothkopf, in preparation.
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