Heavy quarkonium suppression beyond the adiabatic limit

Many prior studies of in-medium quarkonium suppression have implicitly made use of an adiabatic approximation in which it was assumed that the heavy quark potential is a slowly varying function of time. In the adiabatic limit, one can separately determine the in-medium breakup rate and the medium time evolution, folding these together only at the end of the calculation. In this paper, we relax this assumption by solving the three-dimensional Schr\"odinger equation in real time in order to compute quarkonium suppression dynamically. We compare results obtained using the adiabatic approximation with real-time calculations for both harmonic oscillator and realistic complex heavy quark potentials. Using the latter, we find that, for the Υ(1s), the difference between the adiabatic approximation and full real-time evolution is at the few percent level; however, for the Υ(2s), we find that the correction can be as large as 18% in low temperature regions. For the J/Ψ, we find a larger difference between the dynamical evolution and the adiabatic approximation, with the error reaching approximately 36%.