# Heavy quarkonium suppression beyond the adiabatic limit

## TL;DR

This study advances the understanding of quarkonium suppression by solving the 3D Schrödinger equation in real-time, revealing significant deviations from the adiabatic approximation especially for excited states and J/Psi.

## Contribution

It introduces a real-time dynamical approach to quarkonium suppression calculations, moving beyond the traditional adiabatic approximation.

## Key findings

- Real-time evolution differs from adiabatic approximation by up to 36% for J/Psi.
- For Upsilon(1s), the difference is only a few percent.
- The correction can be as large as 18% for Upsilon(2s) in low temperature regions.

## Abstract

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 3d Schrodinger 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 Upsilon(1s), the difference between the adiabatic approximation and full real-time evolution is at the few percent level, however, for the Upsilon(2s), we find that the correction can be as large as 18% in low temperature regions. For the J/Psi, we find a larger difference between the dynamical evolution and the adiabatic approximation, with the error reaching approximately 36%.