Effects of event-by-event hydrodynamic fluctuations on bottomonium dynamics in Pb--Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV
We investigate the effects of event-by-event hydrodynamic fluctuations on bottomonium nuclear modification factors and elliptic flow in Pb--Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV. The internal evolution of the heavy quarkonium is described by a time-dependent Schr\"odinger equation with a temperature-dependent complex heavy-quark potential, while the hot QCD medium evolution is simulated using the iEBE-VISHNU event-by-event viscous hydrodynamic framework. By incorporating both fluctuating and smooth hot media, we find that the bottomonium nuclear modification factor $R_{AA}$ is only marginally affected by event-by-event fluctuations, whereas the elliptic flow $v_2$ is systematically enhanced, with the enhancement growing from the tightly bound $\Upsilon(1S)$ to the more weakly bound $\Upsilon(2S)$ and $\Upsilon(3S)$. This enhancement arises from the more pronounced participant-plane anisotropy of the fluctuating medium relative to the smooth optical-Glauber reference geometry. These results indicate that a smooth hydrodynamic background reproduces the bottomonium $R_{AA}$ but underestimates its $v_2$, so that the bottomonium $v_2$ retains a discernible imprint of event-by-event medium fluctuations.